高計算效率逐步積分法

Step-By-Step Integration Method with High Computational Efficiency

張順益(Shuenn-Yih Chang)

《中國土木水利工程學刊》 25卷3期 (2013/09) Pp. 251-256

https://doi.org/10.6652/JoCICHE.201309_25(3).0007

摘要

由於逐步積分法是非線性動力分析最主要的方法，並且分析所需的計算時間遠大於一般的非線性靜力分析，因此如何提高其計算效率就顯得非常重要。本文將提出新一族具結構相依特性的逐步積分法，此積分法除了具有外顯式積分法的高計算效率之外，也具有一般內隱式積分法的無條件穩定數值特性，除此之外，與一般常用的逐步積分法一樣，具有二階的精確度。這些數值特性使其具有非常優異的計算效率，數值試驗顯示對於一個2000個自由度的結構系統，其所需的CPU時間不到等平均加速度積分法的百分之一而只有千分之六左右，並且隨著自由度的增加，其計算效率更佳。

關鍵字

無條件穩定 ； 二階精確度 ； 外顯式積分法 ； 高計算效率

並列摘要

Since the step-by-step integration method is the most powerful technique for a nonlinear dynamic analysis and it involves much more computational efforts when compared to a nonlinear static analysis, it is important to improve the computational efficiency of the nonlinear dynamic analysis. A novel family of structure-dependent integration methods is proposed herein. It involves no nonlinear iterations, which is the most important advantage for explicit methods, and the unconditional stability, which is the most important advantage for implicit methods. In addition, it also has a second-order accuracy. Consequently, it has very high computational efficiency. In fact, numerical experiments reveal that for a 2000-DOF system, the CPU time involved by the proposed family method is only about 0.6% of that required by the constant average acceleration method. The computational efficiency can become more evident if the number of the degree of the freedom for the analyzed system increases.

並列關鍵字

unconditional stability ； second-order accuracy ； explicit method ； high computational efficiency