本文以平面應變有限元素分析樑的挫曲行為。針對具有相當厚度的樑，以彈性力學為基礎，推導位移型有限元素列式，沒有經過其他的簡化及假設，對於所有的位移邊界條件都能如實加上，與傳統只根據中性面行為的樑理論分析不同，因此應該可以較傳統分析更準確的求得樑在非穩定時的挫曲負荷及模態，對於樑結構的分析具備更佳的精確度與適用性。
本文數值分析結果分別與尤拉樑理論、Timoshenko樑理論以及高階樑理論結果做比較，以了解本文之方法與其他理論之差別，並探討幾何形狀、軸向負載形式以及位移邊界條件對於樑之挫曲強度的影響。

In the present study, the buckling behavior of beams is analyzed by a plane strain finite element. The displacement-type finite element formulation is based on elasticity and has no any other simplification and assumption except that the beam is of moderate depth. Also all the displacement boundary conditions can be imposed exactly. These are the advantages that beam theories of conventional approach, which simulate beams with neutral plane behaviors, do not have. Therefore the present analyses should be able to obtain buckling load and buckling mode more accurately than conventional method.
Numerical values of buckling loads of the present approach will be compared with previously published results of the Euler-Bernoulli beam theory and the Timoshenko beam theory, and further with the high order beam theory to reveal their differences. The effects of the geometry ratio, the distribution of axial loads and the displacement boundary conditions on buckling of beams are also discussed.

摘要 ………………………………………………………………I
目錄 ………………………………………………………………iii
表目錄 ……………………………………………………………v
圖目錄 ……………………………………………………………vii

第一章 緒論 …………………………………………………1
1-1 前言 …………………………………………………1
1-2 文獻回顧 ………………………………………………2
1-2-1 尤拉樑理論 …………………………………………2
1-2-2 Timoshenko樑理論 …………………………………3
1-2-3 高階剪切變形理論 …………………………………5
1-2-4 三維彈性力學分析法 ………………………………6
1-2-5 有限元素法 …………………………………………7

第二章 樑之平面應變有限元素挫曲分析 ……………………8
2-1 前言 …………………………………………………8
2-2 理論推導 ………………………………………………8

第三章 問題解析 ………………………………………………18
3-1 前言 …………………………………………………18
3-2 問題描述 ……………………………………………18
(1) 材料性質 ……………………………………………18
(2) 幾何比例 ……………………………………………18
(3) 邊界條件 ……………………………………………19
(4) 元素選取 ……………………………………………20
(5) 挫曲強度之無因次化 ………………………………20

第四章 結果與討論 ……………………………………………23
4-1 前言 …………………………………………………23
4-2 收斂試驗 ……………………………………………23
4-3 文獻與本文結果之比較與討論 ……………………25

第五章 結論與建議 ………………………………………41
5-1 結論 …………………………………………………41
5-2 建議 …………………………………………………43

參考文獻 …………………………………………………………44
附錄 ………………………………………………………………48

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