结构动力方程的增维精细积分法

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，但对于非齐次动力方程涉及到矩阵求逆的困难。提出采用增维的办法，将非齐次动力方程转化为齐次动力方程，在实施精细积分过程中不必进行矩阵求逆，这种方法对于程序实现和提高数值稳定性十分有利，而且在大型问题中计算效率较高，从而改进了精细积分方法的应用，数值例题显示了本文方法的有效性。

PRECISE TIME-INTEGRATION WITH[1mm］ DIMENSION EXPANDING METHOD

The precise time-integration method proposed for linear time-invariant 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 calculations. Precise time integration with dimensional expanding is proposed in the paper. By using the dimensional expanding, the non-homogeneous vector is viewed as the variables of the equations and the original equations are converted into homogeneous equations. Thus the new method avoids the inverse matrix calculations 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 advantages of the method is remarkable. If the non-homogeneous vector is the solution of one ODEs, the method can give exact results. Otherwise, the methods of constant, linear or sinusoid approximation for the non-homogeneous vector can also give satisfying results. This new algorithm is not only benefit to both the programming implementation and the numerical stability, but also more efficient to large-scale problems. It has improved the precise time-integration method. Numerical examples are given to demonstrate the validity and efficiency of the algorithm.