適用於一般結構動力問題的無條件穩定外顯式積分法

An Unconditionally Stable Explicit Method for General Structural Dynamic Problems

張順益(Shuenn-Yih Chang) ； 許琦偉(Chi-Wei Hsu) ； 楊青昊(Ching-Hao Yang)

《中國土木水利工程學刊》 21卷3期 (2009/09) Pp. 239-246

https://doi.org/10.6652/JoCICHE.200909_21(3).0001

摘要

本文介紹一個新的無條件穩定外顯式積分法，此積分法可應用於一般結構動力問題的求解。其數值特性和先前所發表的無條件穩定積分法相比較，可以發現此新外顯式積分法具有更佳的穩定條件特性，此一數值特性使其可以應用於一般結構動態歷時反應的求解而完全不需考慮穩定條件的問題。因其同時具有外顯式與無條件穩定的數值特性，使其運算效率可以大幅度的提高。不管是數值特性的驗證或是運算效率的比較，都將透過數值釋例的真正求解來加以探究。

關鍵字

無條件穩定 ； 瞬時非線性參數 ； 外顯式積分法

並列摘要

A novel explicit method with unconditional stability is presented. This method can be applied to solve general structural dynamic problems. Although its formulation and numerical properties are very similar to the previously published explicit method, it shows much better stability properties when compared the previously published explicit method. These improved stability properties allow its applications to solve a general structural dynamic problem without considering stability problem. It is very computationally efficient since it has the explicitness of each time step and unconditional stability for general structural dynamic problems. Some numerical examples are used to confirm the numerical properties and computational efficiency.

並列關鍵字

unconditional stability ； instantaneous degree of nonlinearity ； explicit method