Precise integration method without inverse matrix calculation for structural dynamic equations
Precise integration method without inverse matrix calculation for structural dynamic equations
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DOI：
10.1007/s11803-007-0661-2
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发表时间：
2007-03
影响因子：
2.8
通讯作者：
Meng-fu Wang;F. Au
中科院分区：
文献类型：
--
作者：
Meng-fu Wang;F. Au
对于线性时不变齐次动力系统提出的精细积分方法，可以提供在积分点处逼近精确解的精确数值结果。然而，当该算法用于非齐次动态系统时，由于需要求逆矩阵而出现困难。本文将结构动力平衡方程转化为一种特殊形式，用Crout分解法代替矩阵求逆来求解动力平衡方程，得到了不需要求逆矩阵的精细积分法。新算法改进了现有的精细积分方法，提高了计算精度和效率。给出了两个数值算例，验证了该算法的有效性和有效性。
The precise integration method proposed for linear time-invariant homogeneous dynamic systems can provide accurate numerical results that approach an exact solution at integration points. However, difficulties arise when the algorithm is used for non-homogeneous dynamic systems due to the inverse matrix calculation required. In this paper, the structural dynamic equalibrium equations are converted into a special form, the inverse matrix calculation is replaced by the Crout decomposition method to solve the dynamic equilibrium equations, and the precise integration method without the inverse matrix calculation is obtained. The new algorithm enhances the present precise integration method by improving both the computational accuracy and efficiency. Two numerical examples are given to demonstrate the validity and efficiency of the proposed algorithm.