具數值阻尼且為結構相依之逐步積分法的發展

Development of Structure-Dependent Integration Method with Numerical Dissipation

蔡欣芸(Shin-Yun Tsai)

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(2011年)

https://doi.org/10.6841/NTUT.2011.00305

摘要

具數值消散特性的積分法已被認定是逐步積分法的重要發展目標，但目前盛行的幾乎都是內隱式積分法。內隱式積分法雖具有無條件穩定的特色，但其計算效率卻不如外顯式積分法。且內隱式積分法因計算繁複，應用在擬動態實驗上也較不易。本文將介紹新一族具數值消散特性的無條件外顯式積分法，既具有內隱式積分法的無條件穩定優點，亦有外顯式積分法的運算速度，可大幅提高運算效率。更可藉由數值消散特性來抑制數值誤差與實驗誤差所產生的不正確高頻振態反應，成為抑制誤差傳播的有效方式。本文將以線性及非線性的數值論例證實新積分法的數值消散能力，並應用在擬動態實驗上，證明新積分法具有消除因實驗位移控制誤差帶來的不正確高頻反應。

關鍵字

逐步積分法 ； 無條件穩定 ； 擬動態實驗

並列摘要

For the solution of structure dynamic problems, the integration method with numerical dissipation are considered to be important in the development of a new integration method. Although implicit methods can generally have unconditional stability, explicit methods generally preferred over implicit methods since they involve no iteration procedure or extra hardware in the pseudodynamic testing. This paper will propose a new family of unconditionally stable explicit method with numerical dissipation, witch is basted to solving general structural dynamic problems. Due to the explicitness of each time step, this family method involves no nonlinear iteration and thus it is very suitable for both time history analysis and pseudodynamic testing. In addition, many computational efforts can be saved in a time history analysis since there is no nonlinear iteration involved per time step. Both numerical examples and actual pseudodynamic tests are employed to confirm the superiority of the proposed new family method.

並列關鍵字

step-by-step integration method ； unconditional stability ； pseudodynamic tests

參考文獻

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