張氏積分法在歷時分析中的性能表現

使用逐步積分法求解結構動力的問題是目前最普遍的方法。然而逐步積分法又分成內隱式與外顯式兩種，內隱式積分法具有無條件穩定的優點，但是每一步計算較為繁瑣；外顯式積分法則是每一步運算簡潔有效率，但是有條件穩定。因此本文將利用張氏積分法去探討不同結構的動力問題，此積分法不但具有內隱式積分法無條件穩定的優點，亦有外顯式積分法的運算效率，為了證明張氏積分法在實際應用的優越性，本研究將利用美國加州大學柏克萊分校太平洋地震工程研究中心所研發的OpenSees有限元素分析軟體進行模擬，其程式的原始碼為免費及開放性的資源，可以讓程式開發者自行更新與修改程式碼，因此本文將張氏積分法加入於程式中與現有的積分法進行比較，討論張氏積分法廣泛應用於各種不同結構動力問題，不管是簡單的線彈性系統還是複雜的非線性系統，都能有效的求解且能大幅縮短運算的時間，同時也可以利用OpenSees去驗證張氏積分法的數值特性。

關鍵字

外顯式積分法；無條件穩定； OpenSees ；物件導向

並列摘要

The direct integration method might be the most commonly used method for the dynamic analysis. There are two basic categories of direct integration methods. One is explicit and the other is implicit. Although implicit methods can have unconditionally stability their implementations are more complex when compared to explicit methods. On the other hand, in general, explicit methods can only have conditional stability. However, they can have explicit formulations and thus it is computationally efficient for each time step. Thus, either an explicit or an implicit method have its own advantages and disadvantages. Since the Chang explicit method can integrate the most important advantages of explicit and implicit methods together, it is adopted in this study. In order to demonstrate the superiority of Chang explicit method in practical applications, it is implemented into the finite element analysis software OpenSees, which was developed by the researchers at Pacific Earthquake Engineering Research Center, University of California, Berkeley. Consequently, a series of dynamic analyses were conducted by using the Change explicit method and the currently available integration methods. Both linear elastic and nonlinear systems were considered, where the structural nonlinearity may arise from material nonlinearity and/or geometrical nonlinearity. As a result, the feasibility of the Chang explicit method for solving a variety of structural dynamic problems is confirmed. In addition, its superiority of computational efficiency over the currently available integration methods is verified.

並列關鍵字

Explicit Method ； Unconditional Stability ； OpenSees ； Object-Oriented Programming

參考文獻

20. 李宗豪，以有限元素套裝軟體為分析引擎之最佳化設計系統架構開發，碩士論文，國立臺灣大學，呂良正教授指導，台北，2005。

21. 莊明介，結構分析程式物件導向使用者圖形介面之研發，碩士論文，國立臺灣大學，蔡克銓教授指導，台北，2005。

23. 許國志，非線性動力結構分析之GPGPU平行化與效能評估，碩士論文，國立臺北科技大學，楊元森副教授指導，台北，2011。

1. T. Belytschko and T. J. R. Hughes, Computational Methods for Transient Analysis, New York : North-Holland, 1983.

2. M. A. Dokainish and K. Subbaraj, "A survey of direct time-integration methods in computational structural dynamics—I. Explicit methods." Computers & Structures vol. 32, no. 6, 1989, pp. 1371-1386.

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張氏積分法在歷時分析中的性能表現

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