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博碩士論文 etd-0723103-125348 詳細資訊
Title page for etd-0723103-125348
論文名稱
Title
樑之有限元素挫曲分析
Finite Element Buckling Analysis of Beams
系所名稱
Department
畢業學年期
Year, semester
語文別
Language
學位類別
Degree
頁數
Number of pages
75
研究生
Author
指導教授
Advisor
召集委員
Convenor
口試委員
Advisory Committee
口試日期
Date of Exam
2003-06-27
繳交日期
Date of Submission
2003-07-23
關鍵字
Keywords
挫曲、樑、有限元素
buckling, beam, finite element
統計
Statistics
本論文已被瀏覽 5647 次,被下載 20
The thesis/dissertation has been browsed 5647 times, has been downloaded 20 times.
中文摘要
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。
Abstract
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.
目次 Table of Contents
目錄………………………………………………………i
表目錄……………………………………………………iii
圖目錄……………………………………………………vii
摘要………………………………………………………viii
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…………………………………………6
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…………………………………………19
3-1 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………………………………………25
4-1 前言……………………………………………………25
4-2 初始力的影響…………………………………………25
4-3 收斂試驗………………………………………………27
4-4 文獻與本文結果之比較與討論………………………30
第五章 結論………………………………………………69
5-1 結論……………………………………………………69
參考文獻……………………………………………………70
附錄…………………………………………………………75
參考文獻 References
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