適用於一般結構動力問題與擬動態試驗之具數值消散能力的外顯式積分法

由理論分析來求解複雜非線性結構的動態反應是十分困難的事，最常見的方法就是使用逐步積分法。發展擁有數值消散能力的逐步積分法，更是近幾十年積分法發展的重點，因為數值消散特性的逐步積分法已被認為是擬動態試驗上克服因高頻振態所引起誤差累積傳播效應最有效的方式。然而，逐步積分法分成內隱式與外顯式，外顯式運算簡潔有效率，但有穩定條件；內隱式沒有穩定條件，但每一步計算較繁瑣，而且目前擁有數值消散的積分法大多為內隱式。本文提出一個新的外顯式逐步積分法，擁有外顯式積分法的運算效率、二階精確度、無條件穩定與可控制且只會抑制高頻振態而不影響低頻振態的數值消散特性。此新積分法不止適用於一般數值分析，而且也十分適用於擬動態試驗上，用以克服試驗時由於數值誤差或試驗誤差所引起不正確的高頻振態反應。最後本文將經由數例、擬動態試驗與分析來驗證新積分法的優異數值特性。

關鍵字

無條件穩定；數值消散；外顯式積分法；擬動態試驗

並列摘要

Analyzing dynamic responses of complex nonlinear structure systems through theoretical calculation is extremely difficult and the step-by-step integration method is the most frequently adopted way to conduct this analysis. Numerous efforts have recently been made for developing integration algorithm with controllable numerical dissipation in the high-frequency response domain, because it has been recognized that numerical dissipation is an effective way for suppressing the spurious high-frequency modes. Integration algorithms are generally divided into “explicit methods” and “implicit methods.” Explicit methods are computationally efficient, but not unconditionally stable; implicit methods, however, can be unconditionally stable, but their implementation in a computer program is more complex. In general, most integration methods with numerical dissipation are implicit methods. The present study proposes a new explicit integration method which possesses computational efficiency of explicit methods, two order accuracy, unconditional stability, and controllable numerical dissipation that focuses on high-frequency responses but has no impact on low-frequency responses. This method is suitable not only for numerical analyses, but also for pseudodynamic tests due to the existence of numerical dissipation for eliminating the spurious high-frequency response. Furthermore, the study, based on numerical examples, pseudodynamic tests and analyses, supports advantageous numerical characteristics of the new explicit method proposed.

並列關鍵字

Unconditional Stability ； Numerical Dissipation ； Explicit Method ； Pseudodymamic tests

參考文獻

[39] 歐瀚文,HHT-alpha積分法之非線性數值特性,碩士論文,國立臺北科技大學土木與防災研究所,台北,2006。

[40] 廖廸峰,利用瞬時非線性變化程度參數評值逐步積分法的非線性數值特性,碩士論文,國立臺北科技大學土木與防災研究所,台北,2007。

[17] 張順益,“無條件穩定外顯式積分法之發展”,中國土木水利工程學刊,第十三卷,第一期, 2001,第61-70頁.

[1] Belytschko, T., T. J. R. Hughes, Computational methods for transient analysis, Amsterdam Netherlands ; New York, North-Holland Pub, 1983.

[2] Zienkiewicz, O. C., The Finite Element Method, McGraw-Hill, 1977.

國際替代計量

適用於一般結構動力問題與擬動態試驗之具數值消散能力的外顯式積分法

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