具數值消散能力且不需疊代之積分法

A Family of Non-iterative Integration Method with Desired Numerical Dissipation

林士偉(Shih-Wei lin)

指導教授 ： 張順益

國立臺北科技大學/工程學院/土木與防災研究所/碩士(2013年)

https://doi.org/10.6841/NTUT.2013.00013

摘要

以逐步積分法來分析結構動力的問題已經非常的普遍，而具有數值消散特性的逐步積分法更是近年來發展的重要目標。本論文將介紹一個新的逐步積分法，此積分法將具有外顯式積分法的運算效率，以及內隱式積分法的無條件穩定與可以抑制高頻振態而不影響低頻振態的數值消散特性，同時克服外顯式與內隱式積分法之間的缺點。不論是數值消散特性或是運算效率的比較，本論文將以自由振動與強迫振動在線性及非線性的數值論例中加以驗證與討論。最後將應用於擬動態試驗上，證明本積分法在含有高頻振態的擬動態試驗上依然具有良好的數值消散特性及積分的正確性。

關鍵字

外顯式積分法 ； 無條件穩定 ； 數值消散 ； 擬動態試驗

並列摘要

A family of integration methods has been developed for structural dynamics and earthquake engineering. In general, it has unconditional stability and second order accuracy. In addition, it can possess the favorable numerical dissipation properties that can be continuously controlled. In particular, it can have zero damping. This numerical damping is helpful to suppress or even eliminate the spurious growth of high frequency modes while the low frequency modes are almost unaffected. The most important improvement of this family method is that it involves no nonlinear iterations for each time step and thus it is very computationally efficient when compared to a general second-order accurate integration method, such as the constant average acceleration method.
Numerical properties of the proposed family method are obtained through the basic analysis and are confirmed by numerical examples. In addition, its application to pseudodynamic testing is also implemented and a series of actual pseudodynamic tests are performed to confirm the feasibility and superiority of the proposed family method.

並列關鍵字

Explicit Method ； Unconditional Stability ； Numerical Dissipation ； Pseudodynamic test

參考文獻

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