(3.237.20.246) 您好!臺灣時間:2021/04/15 12:36
字體大小: 字級放大   字級縮小   預設字形  
回查詢結果

詳目顯示:::

我願授權國圖
: 
twitterline
研究生:呂學林
研究生(外文):Hsueh-Lin Lu
論文名稱:樑之有限元素挫曲分析
論文名稱(外文):Finite Element Buckling Analysis of Beams
指導教授:劉崇富劉崇富引用關係
指導教授(外文):Chorng-Fuh Liu
學位類別:碩士
校院名稱:國立中山大學
系所名稱:機械與機電工程學系研究所
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:2003
畢業學年度:91
語文別:中文
論文頁數:75
中文關鍵詞:挫曲有限元素
外文關鍵詞:bucklingbeamfinite element
相關次數:
  • 被引用被引用:1
  • 點閱點閱:194
  • 評分評分:系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔系統版面圖檔
  • 下載下載:0
  • 收藏至我的研究室書目清單書目收藏:0
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………………………………………………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
1. S. P. Timoshenko and J. M. Gere, “Theory of elastic stability”, New York, McGraw-Hill, 1961.
2. L. Rayleigh, “The theory of sound”,Dover Publications, New York, vol.1, p.293-294, 1945.
3. C. L. Amba-Rao, “Effect of end conditions on the lateral frequencies of uniform straight columns”, Journal of the Acoustical Socirty of America, vol.42, p.900-901, 1967.
4. R. Frisch-Fay, “On the stability of a strut under uniformly distributed axial forces”, International Journal of Solids and Structures, vol.2, p.361-369, 1966.
5. I. Elishakoff and F. Pellegrini, “Exact and effective approximate solution of some divergent type non-conservative problrms”, Journal of Sound and Vibration, vol.114, p.144-148, 1987.
6. I. Elishakoff and F. Pellegrini, “Application of Bessel and Lommel functions and undetermined multiplier Galerkin method version for instability of non-uniform column”, Journal of Sound and Vibration, vol.115, p.182-186, 1987.
7. M. Eisenberger, “Buckling loads for variable cross-section members with variable axial forces”, International Journal of Solids and Structures, vol.27, p.135-143, 1991.
8. I. Elishakoff and O. Rollot, “New closed-form solutions for buckling of a variable stiffness column by mathematica”, Journal of Sound and Vibration, vol.224, p.172-182, 1999.
9. B. K. Lee and S. J. Oh, “Elastica and buckling load of simple tapered columns with constant volume”, International Journal of Solids and Structures, vol.37, p.2507-2518, 2000.
10. Karam Y. Maalawi, “Buckling optimization of flexible columns”, International Journal of Solids and Structures, vol.39, p.5865-5876, 2002.
11. S. P. Timoshenko, “On the correction for shear of the differential equation for transverse vibrations of prismatic bars”, Phil. Mag. 41, p.744-746, 1921.
12. S. P. Timoshenko, “On the transverse vibrations of bars of uniform cross-section ”, Phil. Mag. 43, p.125-131, 1922.
13. L. E. Goodman and J. G., “Natural frequencies of continuous beams of uniform span length”, Journal of Applied Mechanics, vol.18, p.218-218, 1951.
14. L. E. Goodman, “Flexural vibration in uniform beams according to the Timoshenko theory”, Journal of Applied Mechanics, vol.21, p.202-204, 1954.
15. G. R. Cowper, “The shear coefficient in Timoshenko s beam theory”, ASME, Journal of Applied Mechanics, vol.33, p. 335-340, 1966.
16. J. N. Goodier, “On the problems of the beam and plate in the theory of elasticity”, Transactions of the Royal Society of Canada, vol.32, p.65-88, 1938.
17. A. V. Murty, “Vibrations of short beams”, American Institute of Aeronautics and Astronautics Journal, vol.8, p.34-38, 1970.
18. C. T. Sun, “On the equations for a Timoshenko beam under initial stress”, Journal of Applied Mechanics, vol.37, p. 282-285, 1972.
19. A. Bokaian, “Natural frequencies of beams under axial compressive loads”, Journal of Sound and Vibration, Vol 126, p.49-65, 1988
20. N. G. Stephen, “Beam vibration under compressive axial loads upper and lower bound approximation”, Journal of Sound and Vibration, vol. 131(2), p.345-350, 1989.
21. K. Sato, “On the governing equations for vibration and stability of a Timoshenko beam: Hamilton’s principle”, Journal of Sound and Vibration, vol.145, p.338-340, 1991.
22. V. H. Cortinez and P. A. A. Laura, “An extension of Timoshenko’s method and its application to buckling and vibration problems”, Journal of Sound and Vibration, vol.169, p.141-144, 1994.
23. S. H. Farghaly, “Vibration and stability analysis of Timoshenko beams with discontinuities in cross-section”, Journal of Sound and Vibration, vol.174, p.591-605, 1994.
24. N. G. Stephen and M. Levinson, “A second order beam theory”, Journal of Sound and Vibration, vol.67, p.293-305, 1979.
25. M. Levinson, “A new rectangular beam theory”, Journal of Sound and Vibration, vol.74, p.81-87, 1981.
26. M. Levinson, “Further results of a new beam theory”, Journal of Sound and Vibration, vol.77, p.440-444, 1981.
27. P. R. Heyliger and J. N. Reddy, “A higher order beam finite element for bending and vibration problems”, Journal of Sound and Vibration, vol.126, p.309-326, 1988.
28. B. Aalami, “Waves in prismatic guides of arbitray cross-section”, Journal of Applied Mechanics, vol.40, p.1067-1072, 1973.
29. J. B. Kosmatka, “Transverse vibrations of shear-deformable beams using a general higher order theory”, Journal of Sound and Vibration, vol.160, p.259-277, 1993.
30. H. Matsunaga, “Buckling instabilities of thick elastic beams subjected to axial stresses”, Computers and Structures, vol.59, p.856-868, 1996.
31. H. Matsunaga, “Free vibration and stability of thick elastic beams subjected to axial forces”, Journal of Sound and Vibration, vol.191, p.917-993, 1996.
32. H. Matsunaga, “Vibration and buckling of deep beam-columns on two-parameter elastic foundation”, Journal of Sound and Vibration, vol.228, p.359-376, 1999.
33. L. W. Chen and G. S. Shen, “Vibration and Buckling of initially stressed curved beams”, Journal of Sound and Vibration, vol.215, p.511-526, 1998
34. J. B. Kosmatka, “An improved two-node finite element for stability and natural frequencies of axial-loaded Timoshenko beams”, Computers and Structures, vol.57, p.141-149, 1995.
35. E. J. Barbero, L. A. Godoy and I. G. Raftoyiannis, “Finite elements for three-mode interaction in buckling analysis”, International Journal for Numerical Method in Engineering, vol.39, p.469-488, 1996.
36. M. S. Lake and M. M. Mikulas, “Buckling and vibration analysis of a simply supported column with a piecewise constant cross section”, NASA Technical Paper 3090, 1991.
37. T. A. Morey, E. Johnson and C. K. Shield, “A simple beam theory for the buckling of symmetric composite beams including interaction of in-plane stresses”, Composites Science and Technology, vol.58, p.1321-1333, 1998.
38. R. G. Nair, G. V. Rao and G. Singh, “Stability of a short uniform cantilever column subjected to an intermediate follower force”, Journal of Sound and Vibration, vol.253, p.1125-1130, 2002
39. 簡正和, “樑之平面應變有限元素挫曲分析”, 國立中山大學機械與機電工程研究所碩士論文, 2002
40. J. R. Banerjee and F. W. Williams, “The effect of shear deformation on the critical buckling of columns”, Journal of Sound and Vibration, vol.174, p.607-616, 1994
QRCODE
 
 
 
 
 
                                                                                                                                                                                                                                                                                                                                                                                                               
第一頁 上一頁 下一頁 最後一頁 top
系統版面圖檔 系統版面圖檔