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 本文以平面應變有限元素分析樑的挫曲行為，以二維彈性力學理論推導出位移型有限元素列式，並整理成典型特徵值形式，再經過變數轉換，改寫成另一種特徵值列式，以避免求特徵值所需之疊代以及疊代過程中計算所可能造成的困擾，而且也可以一次求得多個挫曲值；和傳統樑理論比較，由於本文是基於彈性力學，除了要求樑之寬厚比須有相當比值，以符合平面應變之條件外，並無經過額外假設，因此理論上應比傳統樑理論更加準確；由於本文在求取挫曲強度的程式運算時間上，比疊代逼近法少許多，若能達到同樣之精確度，則本法比疊代逼近法有更高的適用性。 本文數值分析結果將和疊代逼近求解法、尤拉樑理論、Timoshenko樑理論以及高階樑理論結果做比較，以驗證本文之正確性，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 based on two-dimensional elasticity of a buckling beam leads to an eigenvalue problem and is transformed again into another type of eigenvalue problem to eliminate iterations and possible difficulty during iterations and to obtain the various critical loads simultaneously.Comparing with conventional beam theories, the present approach needs no approximations or assumptions except that the width-to thickness ratio should be large enough for the beam to be considered as a plane strain case. Theoretically the present method should be more accurate than conventional beam theories and attractive than iterative method if the same accuracy is obtained, due to the economy in computation of the present method.Buckling strength under different beam geometry, type of loading, and boundary condition by the present approach will be compared with those by iterative method and various beam theories to test its validation and accuracy.
 目錄………………………………………………………i表目錄……………………………………………………iii圖目錄……………………………………………………vii摘要………………………………………………………viii第一章 緒論………………………………………………11-1 前言……………………………………………………11-2 文獻回顧………………………………………………21-2-1 尤拉樑理論…………………………………………21-2-2 Timoshenko樑理論…………………………………31-2-3 高階剪切變形理論…………………………………51-2-4 三維彈性力學分析法………………………………61-2-5 有限元素法…………………………………………6第二章 樑之平面應變有限元素挫曲分析………………82-1 前言……………………………………………………82-2 理論推導………………………………………………8第三章 問題解析…………………………………………193-1 問題描述………………………………………………19(1) 材料性質………………………………………………19(2) 幾何比例………………………………………………19(3) 邊界條件………………………………………………20(4) 元素選取………………………………………………21(5) 挫曲強度之無因次化…………………………………21第四章 結果與討論………………………………………254-1 前言……………………………………………………254-2 初始力的影響…………………………………………254-3 收斂試驗………………………………………………274-4 文獻與本文結果之比較與討論………………………30第五章 結論………………………………………………695-1 結論……………………………………………………69參考文獻……………………………………………………70附錄…………………………………………………………75
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 1 樑之平面應變有限元素挫曲分析 2 抗彎構架中H型鋼梁之挫屈行為 3 梁元素之一致性共旋轉有限元素推導法及其應用 4 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 5 樑式結構之分散吸振器設計分析 6 含脫層複材疊層樑之接觸及局部挫曲分析與實驗 7 應用有限元素法於圓截面複合材料疊層桿件所組成剛架結構之大變形的研究 8 軸壓作用下薄殼圓柱挫屈應力之有限元素法分析 9 三跨距階梯樑之動態響應分析 10 樑的混合型平面應變有限元素振動分析 11 以接納法分析組合結構之彈性挫曲特性 12 雷射圓管成形之皺曲現象研究 13 複合材料薄壁樑元素之應用 14 梁在與變位相關的負荷作用下之挫屈後行為分析

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 1 樑之平面應變有限元素挫曲分析 2 三跨距階梯樑之動態響應分析 3 樑受預應力之平面應變有限元素振動分析 4 管內非軸對稱層對T(0,1)扭矩模態之影響 5 利用挫曲變形量測殘餘張應力之新型測試鍵 6 挫屈梁之靜態與動態分析 7 船艏波擊力作用下之艏結構挫曲強度分析 8 利用傅立葉配置法求解橢圓及特徵值問題 9 關於隨機股價之選擇權價值之有限體積法 10 Black-Scholes公式及其推導 11 低轉速平面發電機研究 12 熱效應於銅銲線接合製程之有限元素法模擬 13 高爾夫球桿頭撞擊聲音之分析 14 雷射熱破裂技術於切割脆性材料之模擬分析 15 薄板壓延之有限元素分析及擴寬預測式之決定

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