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研究生:黃郁青
研究生(外文):Yu-Ching Huang
論文名稱:自動判別之內部載重及束制
論文名稱(外文):Loading and Constraint for Automatic Mesh
指導教授:潘誠平
指導教授(外文):Chan-Ping Pan
學位類別:碩士
校院名稱:國立臺灣科技大學
系所名稱:營建工程系
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:中文
論文頁數:65
中文關鍵詞:等值節點力內部非節點載重及束制自動網格佈建有限元素法
外文關鍵詞:Equivalent LoadingInternal Loading and ConstraintAutomatic MeshFinite Element
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本論文主要是將等值節點力的理論以及考慮內部束制條件會造成總體勁度矩陣改變之影響加入有限元素法之程式中,其中包含了以下之探討:(1)將真實平面上某一點座標,反算其所對應於標準元素上之座標,並自動搜尋其所屬之元素;(2)點載重、線載重之等值節點力,並使線載重跨元素;(3)束制條件點彈簧、線彈簧之探討。
本研究之成果讓使用者可任意輸入載重及束制條件而不必考慮載重及束制條件必須加在節點或元素邊緣的限制,亦不須指明位於哪一個元素之內部,透過程式內部的運算將元素內部載重分給所屬元素的各個節點,並自動將內部束制條件造成改變的總體勁度矩陣求出並求解,免除了使用者輸入載重及束制條件時,須經過位置座標的計算才能得到載重及束制條件位於何節點及元素上的複雜繁瑣的前置輸入作業,因此提昇使用者的便利性。

The core of this research is to make use of the theory of Equivalent Loading and to considering the effect of internal constraint. The change of the stiffness matrix is implemented to Finite Element Formulation. This involves three stages:
1.Calculate and map a specific point in the real plane to its coordinate in the master element, and search for its element automatically.
2.Figure out the equivalent loading of the point loading and the curved line loading, and then make the line loading cross elements.
3.Figure out the formulation of constraint of point spring and line spring.
The achievement of this research is to allow the user an easy way to input the loading and constraint without the limit to put them in the joint or the edge of an element. There is no need to indicate it to certain element, either. The internal calculation of this formula will automatically distribute the internal loading of an element to its joints, and calculate the modified stiffness according to the internal constraint.

第一章 緒論 1
1-1 研究動機與目的 1
1-2 文獻回顧 2
1-3 本文架構 4
第二章 網格自動佈建 5
2-1 區塊定義 5
2-2 區塊內自動切割元素 6
2-3 網格的調適 7
2-4 此網格佈建法之輸入及輸出 8
2-5 結論 8
第三章 理論及解析流程介紹 10
3-1 前言 10
3-3 等值節點力的推導 11
3-3-1 真實元素映射至標準元素 11
3-3-2 點集中載重的等值節點力 13
3-3-3 曲線段均佈載重的等值節點力 15
3-4 元素內部非節點之彈簧 19
3-4-1 元素內部點彈簧 19
3-4-2 元素內部線彈簧 22
3-5 跨元素之線載重 26
第四章 程式驗證與案例探討 29
4-1 前言 29
4-2 有限元素樑模型的建立 29
4-3 比較與驗證 30
4-3-1 內部非節點集中載重之驗證 30
4-3-2 內部非節點均佈載重之驗證 30
4-3-3內部非節點點彈簧之驗證 31
4-4 案例探討 31
4-4-1 前言 31
4-4-2 點彈簧彈性模數值增大至成為鉸接支承之探討 32
4-4-3案例探討結論 32
4-5 結論 33
第五章 結論與建議 34
5-1 本研究之結論 34
5-2 未來之研究方向 35
參考文獻 36
附錄 64

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