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研究生:許碩修
研究生(外文):Shuo-Hsiu Hsu
論文名稱:雙對稱薄壁梁在軸力與不均勻彎矩作用下的側向-扭轉挫屈分析
論文名稱(外文):Lateral-Torsional Buckling Analysis of Bisymmetric Thin-Walled Beam under Axial Force and Nonuniform Bending Moment
指導教授:蕭國模
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程系
學門:工程學門
學類:機械工程學類
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:148
中文關鍵詞:挫屈側向-扭轉挫屈
外文關鍵詞:beambucklinglateral-torsional buckling
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本研究的主要目的是探討雙對稱薄壁梁在軸向力及不均勻彎矩同時作用下的非線性側向-扭轉挫屈分析。
本研究採用文獻[1]的梁元素,在文獻[1]中利用共旋轉法,虛功原理及非線性梁理論之二階一致線性化來推導梁元素。
本文解非線性平衡方程式的數值計算方法是基於牛頓-拉福森(Newton-Raphson)法配合弧長控制(arc length control)法的增量迭代法。本研究中以系統切線剛度矩陣之行列式值為零當作挫屈準則,利用弧長的二分法求得挫屈負荷。
本研究中探討了不同斷面、長度、邊界條件的梁在軸力及各種不均勻彎矩作用下的側向-扭轉挫屈彎矩及挫屈後行為,並驗證文獻上線性挫屈分析結果的正確性。

In the study, the nonlinear lateral-torsional buckling analysis of bisymmetric thin-walled beam under axial force and nonuniform bending moment is investigated.
The beam element developed in reference [1] is employed here. In reference [1], the co-rotational formulation, the virtual displacement method and the consistent second order linearization of geometric beam theory are used.
An incremental-iterative method based on the Newton-Raphson method combined with constant arc length of incremental displacement vector is employed for the solution of nonlinear equilibrium equations. The zero value of the tangent stiffness matrix determinant of the structure is used as the criterion of the buckling state. A bisection method of the arc length is used to find the buckling load.
The nonlinear lateral-torsional buckling moment and post buckling behavior of beams with different sections, lengths, and boundary conditions under axial force and nonuniform bending momen is investigated. The accuracy of results of the linear buckling analysis given in the literature is examined.

中文摘要 ..…………………………………………………………… Ⅰ
英文摘要 ..…………………………………………………………… Ⅱ
誌謝 ………………………………………………………………….. Ⅳ
目錄 ………………………………………………………………….. Ⅴ
表目錄 ……………………………………………………………..… Ⅶ
圖目錄 ……………………………………………………………..… ⅩⅡ
第一章 緒言 ………………………………………………………… 1
第二章 理論推導 ………………………………………………….. 4
2.1 基本假設 …………………………………………………….. 4
2.2 座標系統 …………………………………………………….. 4
2.3 梁元素之位移與應變 ……………………………………….. 5
2.4 節點參數與節點力 ………………………………………….. 8
2.4.1 元素節點參數與節點力 ……………………………….. 8
2.4.2 元素顯節點參數的擾動與隱節點參數的擾動關係 ….. 9
2.4.3 元素顯節點內力與隱節點內力的關係……………….… 10
2.5 元素隱節點內力之推導 ……………………………………. 10
2.6 元素剛度矩陣 ……………………………………….………. 12
2.7 系統平衡方程式與收斂準則 ……………………………….. 14
第三章 數值計算方法與程序 …………………………………….. 16
3.1 增量迭代法 ………………………………………………….. 16
3.2 二分法 ……………………………………………………….. 17
3.3 N循環迭代法 ………………………………………………… 18
第四章 數值例題 …………………………………………………… 20
4.1 問題的描述 …………………………………………………… 20
4.2 收斂分析 ……………………………………………………… 22
4.3 個案分析 ……………………………………………………… 22
第五章 結論與展望 ………………………………………………… 25
參考文獻 ……………………………………………………………. 27
附表 ………………………………………………………………….. 30
附圖 ………………………………………………………………….. 97
附錄A 簡支梁的側向挫屈軸力 …………………………………… 138
附錄B 簡支梁的扭轉挫屈軸力 …………………………………… 140
附錄C 斷面常數 …………………………………………………… 141
附錄D 簡支梁及懸臂梁之線性挫屈彎矩 ………………………… 147

參考文獻
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8. Gendy A.S., and Saleeb A.F., “Generalized Mixed Finite Element Model for Pre- and Post-Quasistatic Buckling Response of Thin-Walled Framed Structures,” Int. J. Num. Meth. Eng., 37, pp. 297-322, 1994.
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14. Horne M.R., “The Flexural-Torsional Buckling of Members of Symm. I-Sect. Under Comb. Thrust and Unequal Terminal Moments,” Q. J. Mech. Appl. Math., 7, Part 4, 1954.
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22. 林志聰, 梁在軸力及彎矩作用下的側向-扭轉挫屈分析, 交通大學機械工程研究所碩士論文, 臺灣, 新竹, 2001.
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