臺灣博碩士論文加值系統

一般分析樑結構大多以Euler樑理論為基礎，其忽略了剪力對樑結構的影響，因為大部分樑結構的跨深比較大，所產生的剪力效應相對的小；當分析跨深比較小的樑結構，或是具有較明顯的剪力效應結構時，剪力效應就必須考慮，於是本文應用了Timoshenko樑理論來分析跨深比較小的樑結構。
　　向量式有限元素法為新穎的數值計算方法，不需求解矩陣方程組及疊代計算，大量減少了數值分析中所必須面對的困難，本文以向量式有限元素法來推導Timoshenko樑元素以分析短跨距深樑結構物。由早先樑理論的文獻可知，Euler樑理論忽略了剪力效應，因此我們將向量式有限元素法的基礎理論改為有加入剪力效應的Timoshenko樑理論，探討向量式有限元素法是否能夠應用Timoshenko樑理論來分析結構物。
　　本文以向量式有限元素法應用Timoshenko樑理論的數值方法，分析的結構有深樑、簡支樑、懸臂樑及門型剛架。簡支樑、懸臂樑及門型剛架的靜力分析驗證本文理論及程式計算的正確性；深樑的靜力分析與Ahmed(1996)利用有限差分法的數值做比對；並以簡支樑、懸臂樑及門型剛架的動力分析，探討改變跨深比及外力條件的分析結果。

In this study, a vector form intrinsic finite element (VFIFE) is derived and applied to study both the static and dynamic responses of deep short beams under dynamic loadings. It is already known that the application of classical beam theory known as Euler’s beam theory to beams with large ratio of D/L (depth/span larger than 1/4), a short-deep beam, may not necessarily obtain satisfactory results for the stress analysis of the beam. One of the main presumptions from the classical Euler’s beam theory is that the plane of the cross-section remains plane and normal to the neutral axis of the beam after deformation. This presumption is no more true when the beam subject to loadings is a short-deep beam because the bending stress is no longer a dominant stress while the other secondary effects may have more severe influences on the mechanical behavior of the beam. This study by utilizing the vector form intrinsic finite element method (VFIFE) to derive a new element for the Timoshenko beam provides an alternative method for the analysis of a short-deep beam, particularly, subject to dynamic loadings. By taking the advantage of the VFIFE that is a time-saving scheme for the dynamic analysis, the element of Timoshenko-beam is derived along with the dynamic solution procedure. The motions in transverse direction and the rotation at each node of the beam are calculated and presented into figures. The results from numerical analysis are also verified with theoretical solution (exact analytical solution) and further compared to the results obtained from traditional finite element method.

總目錄 i
圖目錄 iii
表目錄 viii
第一章 緒論 1
1.1 文獻回顧與研究動機 1
1.2 向量式有限元研究背景 4
1.3 本文內容 5
第二章 向量式有限元基本理論與Timoshenko樑理論 9
2.1 向量式有限元素法的離散化 9
2.2 平面剛架元節點變形及座標系統(deformation coordination system) 10
2.3 平面剛架元的增量內力計算 13
2.3.1 Timoshenko樑理論 13
2.3.2 Timoshenko樑理論應用於向量有限元的增量內力計算 14
2.4 平面剛架元質點運動方程式的差分式 19
2.5 顯式時間積分 21
2.6 計算流程 23
第三章 結果與討論 27
3.1 向量有限元靜力分析 27
3.1.1 向量有限元基本驗證 27
3.1.2 深樑分析 29
3.2 動力分析 29
3.2.1 理想階梯負載(Ideal Step Loading) 30
3.2.2 脈衝負載(Impulse Loading) 31
3.2.3 諧合負載(Harmonic Loading) 32
3.2.4 地震力(Earthquake Loading) 33
第四章 結論與建議 84
4.1 結論 84
4.2建議 85
附錄 A 86
參考文獻 90

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