臺灣博碩士論文加值系統

在本論文中，探討Hilber、Hughes與Taylor所提出的積分法(簡稱HHT-α積分法)在求解非線性結構系統時的數值特性，為了要評估非線性系統，本論文定義兩個新參數，其中一個參數名為單步非線性變化程度(step degree of nonlinearity)，用來描述結構勁度在積分時間步長內的變化情形；另一個參數名為收斂度(step degree of convergence)，用來描述非線性系統逐步積分求解的反覆疊代過程中，其收斂勁度與正確勁度的接近程度。在引入這兩個新參數後，HHT- 積分法應用於非線性系統時，才能評估其數值特性。
因為非線性關係的考量，在實際計算時可有兩種不同的計算方式。方法一為HHT-α積分法的運動方程式中，其勁度被假設使用同樣的 ，而方法二在實際的運用上將HHT-α積分法的運動方程式之勁度跟隨著位移而定。本文利用這兩個方法，進一步探討HHT-α積分法在求解非線性結構系統的數值特性。
本文使用數值釋例證實評估結果，在基本的評估後，本文推斷方法一在任何的單步非線性變化程度和收斂度之下都是無條件穩定，而且不管是在線彈性或非線性系統之下都擁有數值消散特性；而方法二在內部勁度軟化的情況下，會發生數值的不穩定。所以經過這些評估可以驗證方法一比方法二具有較好的數值特性。

目　錄

摘　要 i
ABSTRACT ii
誌　謝 iv
目　錄 v
圖目錄 vi
第一章　緒　論 1
1.1 研究動機與目的 1
1.2 文獻回顧 3
1.3 研究內容概述 3
第二章　HHT-α積分法 5
2.1 HHT-α積分法簡介 5
2.2 HHT-α積分法的線性數值特性 6
第三章　HHT-α積分法之非線性數值特性 9
3.1 方法一的數值特性 10
3.2 方法二的數值特性 15
3.3 數值特性比較 19
第四章　HHT-α積分法之數值模擬 36
4.1 數值釋例一 36
4.1.1 給定初始位移之兩層剪力屋架 37
4.1.2 受到一簡諧荷重之兩層剪力屋架 38
4.2 數值釋例二 39
4.2.1 自由振動下之兩層剪力屋架 39
4.2.2 自由振動下之五層剪力屋架 40
第五章　結　論 60
參考文獻 61

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