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系統識別號 U0026-0812200910360192
論文名稱(中文) 有限元素法波場模式之延伸
論文名稱(英文) Extension of Wave Modeling in Finite Element Method
校院名稱 成功大學
系所名稱(中) 水利及海洋工程學系碩博士班
系所名稱(英) Department of Hydraulics & Ocean Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 蔡金晏
學號 n8689104
學位類別 碩士
語文別 中文
口試日期 2002-05-31
論文頁數 68頁
口試委員 口試委員-楊德良
口試委員-莊文傑
口試委員-岳景雲
指導教授-許泰文
關鍵字(中) 碎波
有限元素法
緩坡方程式
關鍵字(英) wave breaking
mild-slope equation
finite element method
學科別分類
中文摘要 本文針對橢圓型態之緩坡方程式,以有限元素法建立波浪數值模式,模式中考量波浪於近岸傳遞時可能因地形及結構物產生能量消散等變化,擬將模式延伸至包含非線性淺化、碎波及潛式透水結構物等範疇。模式建立時所採用之邊界條件為近似輻射邊界條件,而外海開放邊界條不等水深處,則是沿用許等人 (2001) 所提出之不等水深輻射邊界條件予以設定。文中主要探討各碎波指標及碎波能量消散項應用於模式之適用性,並進一步加入非線性淺化修正項以改善線性淺化公式於描述波浪碎波波高之不足。此外,考慮實際應用時可能面臨之潛式透水結構物問題,於緩坡方程式中加入透水介質效應以期能反應出波浪於透水結構物中能量之損失效應。經由波浪通過各式斜坡底床地形的校核計算,結果經與實驗數據之比較顯示應用McCowan (1894) 及Dally等人 (1985) 之碎波指標及碎波能量消散公式模擬波浪於斜坡上碎波所獲結果較為滿意,而非線性淺化修正項亦提升能模式預測碎波點附近波高之精確性。此外,對於波浪通過透水潛堤之測試中,顯示考慮透水效應之波場模式可以得到與實驗數據相近之計算結果。
英文摘要 A numerical model based on elliptic mild–slope equation is developed using finite element method. The model is extended to include the effects of wave breaking, nonlinear shoaling and waves propagating over a submerged permeable breakwater. The radiation boundary condition is approximated to the second-order term for wave with large angle incidence. On the open boundaries with varying depth, the boundary conditions proposed by Hsu et al. (2001) is adopted. To verify the validity of the present model, cases of wave propagating over different sloping beaches were run using the developed computer program. The results show that the wave criteria addressed by McCowan (1894) and by Dally et al. (1985) provide more accurate predictions in the numerical calculation. Furthermore, numerical results also show that the addition of nonlinear shoaling term in the mild-slope equation could improve underestimation of wave height around the breaking point. The model is also examined for the cases of waves passing over submerged permeable breakwaters. Model results are well compared with the experimental data.
論文目次 中文摘要...............................................I
英文摘要..............................................II
致謝.............................................III
目錄..............................................IV
圖目錄..............................................VI
表目錄............................................VIII
符號說明..............................................IX
第一章 緒論...............................................1
 1-1 研究動機與目的...............................................1
 1-2 前人研究...............................................4
 1-3 本文組織...............................................8
第二章 理論基礎...............................................9
 2-1 緩坡方程式...............................................9
 2-2 含透水介質效應之緩坡方程式..............................................10
 2-3 邊界條件..............................................11
  2-3-1 近似輻射邊界條件..............................................13
  2-3-2 全反射、部分反射或全透射邊界條件..............................................14
  2-3-3 外海開放邊界條件..............................................15
 2-4 碎波指標與碎波能量消散項..............................................17
 2-5 非線性淺化修正項..............................................18
第三章 數值模式..............................................21
 3-1 離散方程式..............................................21
 3-2 有限元素法..............................................26
  3-2-1 二次形狀函數..............................................26
  3-2-2 領域積分..............................................28
  3-2-3 邊界積分..............................................28
 3-3 計算流程..............................................30
第四章 結果與討論..............................................32
 4-1 碎波指標與碎波能量消散項之測試..............................................32
  4-1-1 波浪正向入射等坡度斜坡底床..............................................34
  4-1-2 波浪正向入射複合式斜坡底床..............................................46
  4-1-3 綜合討論..............................................52
 4-2 非線性淺化修正項之測試..............................................53
 4-3 透水介質效應之測試..............................................56
第五章 結論與建議..............................................63
 5-1 結論..............................................63
 5-2 建議..............................................64
參考文獻..............................................65
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4. Berkhoff, J.C.W., Booij, N., Radder, A.C., "Verification of Numerical Wave Propagation Models for Simple Harmonic Linear Water Waves," Coastal Engineering, Vol. 6, pp. 255-279 (1982).
5. Bettess, P. and Zienkiewicz, O.C., "Diffraction and Refraction of Surface Waves Using Finite and Infinite Element," International Journal for Numerical Methods in Engineering, Vol. 11, pp. 1271-1290 (1977).
6. Booij, N., "Gravity Waves on Water with Non-uniform Depth and Current," Delft University of Technology, Department of Civil Engineering, Report No. 81-1, (1981).
7. Battjes, J.A. and Janssen, J., "Energy loss and set-up due to breaking of random waves," Proceedings of 16th International Conference on Coastal Engineering, pp. 569-587 (1978).
8. Black, K.P. and Rosenberg, M.A., "Energy loss and set-up due to breaking of random waves," Proceedings of 16th International Conference on Coastal Engineering, pp. 569-587 (1978).
9. Chen, H.S. and Mei, C.C., "Oscillation and Wave Force on an Offshore Harbor," Ralph M. Parsons Laboratory, Massachussetts Institute of Technology, Report No. 190 (1974).
10. Copeland, G.J.M., "A Practical Alternative to the Mild-slope Wave Equation," Coastal Engineering, Vol. 9, pp. 125-149 (1985).
11. Dally, W.R., Dean, R.G., Dalrymple, R.A., "Wave Height Variation Across Beaches of Arbitrary Profile, " Journal of Geophysical Research, Vol. 90, pp. 11917-11927 (1985).
12. Dalrymple, R.A., Suh, K.D., Kirby, J.T., Chag, J.W., "Models for Very Wide-Angle Water Waves and Wave Diffraction. Part 2. Irregular Bathymetry," Journal of Fluid Mechanics, Vol. 201, pp. 299-322 (1989).
13. Dingemans, M.W., "Verification of Numerical Wave Propagation Method with Field Measurements:CREDIZ Verification Haringvliet," Rep W488, pt. 1, Delft Hydraulic Laboratory, Delft (1983).
14. Goda, Y., "Irregular Wave Deformation in the Surf Zone," Coastal Engineering In Japan, Vol. 18, pp. 13-26 (1975).
15. Hsu, T.W., and Wen, C.C., "On the Parabolic Approximation for Water Wave Transformation," 19th Ocean Engineering, Taichung, pp. 97-104 (1997).
16. Hsu, T.W., and Wen, C.C., "A Study of Using Parabolic Model to Describe Wave Breaking and Wide-angle Wave Incidence," Journal of the Chinese Institute of Engineers, Vol. 23, No. 4, pp. 515-527 (2000).
17. Isaacson, M., and Qu, S., "Waves in a Harbour with Partially Reflection Boundaries." Coastal Engineering, Vol. 14, pp. 193-214 (1990).
18. Ito, Y. and Tanimoto, K., "A Method of Numerical Analysis of Wave Propagation Application to Wave Diffraction and Refraction," Proceedings of 13th International Conference on Coastal Engineering, pp. 503-522 (1972).
19. Isobe, M., "A Parabolic Equation Model for Transformation of Irregular Waves due to Refraction, Diffraction and Breaking," Coastal Engineering in Japan, Vol. 30, pp. 33-47 (1987).
20. Kirby, J.T., "Higher-Order Approximations in the Parabolic Equation Method for Water Waves," Journal of Geophysical Research, Vol. 91, pp. 933-952 (1986a).
21. Kirby, J.T., "Rational Approximations in the Parabolic Equation Method for Water Waves," Coastal Engineering, Vol. 10, pp. 355-378 (1986b).
22. Le Mehaute, B. and Wang, J.D., "On the Breaking of Waves Arriving at an Angle to the Shore," Journal of Fluid Mechanics, Vol. 141, pp. 265-274 (1984).
23. Li, B., "An Evolution Equation for Water Waves, " Coastal Engineering, Vol. 23, pp. 227-242 (1994).
24. Liu, P.L.F., "Damping of Water Waves Over porous Bed," Journal of Hydraulic Division, Vol. 99, pp. 2263-2271 (1987).
25. Losada, I.J., Silva, R., Losada, M.A., "Interaction of Non-breaking Directional Random Waves with Submerged Breakwaters," Coastal Engineering, Vol. 28, pp. 249-266 (1996).
26. Madsen, P.A. and Larsen, J., "An Efficient Finite-Diffraction Approach to the Mild-slope Equation," Coastal Engineering, Vol. 11, pp. 329-351 (1987).
27. Mase, H. and Iwagaki, Y., "Wave Height Distribution and Wave Grouping in Surf Zone," Proceedings of 18th International Conference on Coastal Engineering, pp. 52-78 (1982).
28. McCowan, J., "On the Highest Wave of Permanent Type," Philos. Mag. Edinburgh, 38(5), pp. 351-358 (1894).
29. Nagayama, S., "Study on the Change of Wave Height and Energy in the Surf Zone," Bachelor thesis, Yokohama National University, 80pp. (1983).
30. Panchang, V.G., Chen, W., Xu, B., Schlenker, K., Demirbilek, Z., Okihiro, M., "Exterior Bathymetric Effects in Elliptic Harbor Wave Models", Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 126, pp. 71-78 (2000).
31. Panchang, V.G., Pearce, B.R., Ge, W., Cushman-Roisin, B., "Solution of the Mild-Slope Wave Problem by Iteration," Applied Ocean Research., 13(4). pp. 187-199 (1991).
32. Radder, A.C., "On the Parabolic Equation Method for Water Wave Propagation," Journal of Fluid Mechanics, Vol. 95, pp. 159-176 (1979).
33. Rojanakamthorn, S., Isobe, M., Watababe, A., "A Mathematical Model of Wave Transformation Over a Submerged Breakwater," Coastal Engineering in Japan, Vol. 32, pp. 209-234 (1989).
34. Shuto, N., "Nonlinear Long Waves in a Channel of Variable Section," Coastal Engineering in Japan, Vol. 17, pp. 1-12 (1974).
35. Sollitt, C.K. and Cross, R.H., "Wave Transmission Through Permeable Breakwaters," Proceedings of 13th International Conference on Coastal Engineering, pp. 1827-1846 (1972).
36. Watanabe, A. and Maruyama, K., "Numerical Modeling of Nearshore Wave Field under Combined Refraction, Diffraction and Breaking," Coastal Engineering in Japan, Vol. 29, pp. 19-39 (1986).
37. Zhao, L., Panchang, V.G., Chen, W., Demirbilek, Z., Chhabbra, N., "Simulation of Wave Breaking Effects in Two-dimensional Elliptic Harbor Wave Model," Coastal Engineering, Vol. 42, pp. 359-373 (2001).
38. 林貴斌,「以有限元素法模擬大角度入射之波場」,國立成功大學水利及海洋工程研究所碩士論文 (2000)。
39. 郭一羽主編,「海岸工程學」,文山書局,第149頁-第153頁 (2001)。
40. 許泰文,蔡丁貴,顏朝卿,陳伯旭,「以有限元素法模擬近岸波場」,第二十屆海洋工程研討會論文集,第491頁-第499頁 (1998)。
41. 許泰文,藍元志,林貴斌,「以有限元素法模擬大角度入射之波浪變形」,第二屆國際海洋大氣會議論文彙編-海洋,第160-165頁 (2000)。
42. 許泰文,藍元志,王永和,「以有限元素法模擬波浪變形」,第十二屆水利工程研討會論文集,第I37-I44頁 (2001)。
43. 陳伯旭,蔡丁貴,「局部輻射邊界條件在水波數值模式上之應用」,第十二屆海洋工程研討會論文集,第1頁-第9頁 (1990)。
44. 陳伯旭,蔡丁貴,「以有限元素法模擬模擬近岸碎波波場」,八十六年度海岸工程數值模式研討會論文集,第29頁-第40頁 (1997)。
45. 溫志中,「修正緩坡方程式之研發與應用」,國立成功大學水利及海洋工程研究所博士論文 (2001)。
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系統識別號 U0026-0812200910402717
論文名稱(中文) 新型三維六面體元素之研究
論文名稱(英文) The Study of The New Three-Dimensional Hexahedral Elements
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 何信葳
學號 n1690424
學位類別 碩士
語文別 中文
口試日期 2003-07-09
論文頁數 62頁
口試委員 口試委員-褚晴暉
指導教授-何旭彬
口試委員-吳學鑑
關鍵字(中) 疊代法
有限元素法
三維六面體元素
靜態縮減法
關鍵字(英) three-dimensional hexahedral elements
finite element method
static condensation
iterative method
學科別分類
中文摘要 本文提出一種新類型的三維六面體元素,發現其與傳統常用的一階8節點元素、二階Serendipity 20節點元素及二階Lagrange 27節點元素比較,其精確度較準且求解時間較短。
本文中的新型元素在一階至三階的Serendipity元素內部,增加額外的節點,使得在元素的邊上仍為一階至三階內插函數,但元素的內部為更高階的內插函數,因而提高了元素的精確度。由於這些額外增加的內部節點,不與其他元素相接,故在元素勁度矩陣形成後,這些內部節點所對應的矩陣成分,即是整體勁度矩陣的最後矩陣成分。因此在元素勁度矩陣形成後,即可使用高斯消去法將內部節點對應的行、列先消去。在組成整體勁度矩陣求解時,本研究發現,疊代法比高斯消去法快很多。此新型元素所形成的整體勁度矩陣,所需疊代次數較少,故求解時間也較短。
在實例測試中,與各階Serendipity元素相比,發現一階內部含1節點新元素誤差相對下降38%,計算速度快1%;二階內部含8節點新元素誤差相對下降38%,計算速度快20%;三階內部含27節點新元素相對誤差下降69%,計算速度快35%。
英文摘要 A family of new three-dimensional hexahedral elements is proposed in this thesis. When compared with the linear 8 nodes element, quadratic Serendipity 20 nodes element, and quadratic Lagrange 27 nodes element, these new elements spent less computational time and got less approximation errors.
The idea for these new elements is using extra nodes in the interior of the hexahedral elements to get high order interpolation functions in the elements. When the element equations are formed, the equations corresponding to these interior degrees of freedom can be eliminated by static condensation. When global system equations are solved, we found that iterative method is much faster than the Gauss elimination method. When new elements are used, less iterative number is needed compared Serendipity elements and Lagrange elements.
Compared with the Serendipity elements, the error of the linear new element drops 38% and its computational time drops 1%. The error of the quadratic new element drops 38% and its computational time drops 20%. The error of the cubic new element drops 69% and its computational time drops 35%.
論文目次 中文摘要....................................................i
英文摘要...................................................ii
誌謝......................................................iii
目錄........................................................v
表目錄...................................................viii
圖目錄......................................................x
符號說明...................................................xi




第一章 緒論............................................1
1.1 前言.............................................1
1.2 文獻回顧.........................................2
1.3 研究動機與目的...................................3
1.4 論文架構.........................................4
第二章 相關理論.........................................6
2.1 三維彈性力學.....................................6
2.2 元素的型態......................................10
2.2.1 Lagrange型態元素...........................11
2.2.2 Serendipity型態元素........................12
2.2.3 H型態元素..................................14
2.3 靜態縮減矩陣....................................20
2.4 求解線性聯立方程組..............................21
2.4.1 預加條件共軛梯度法..........................22
2.4.2 預加條件....................................22
2.5 誤差分析與收斂的定義............................24
第三章 程式驗證與問題描述..............................27
3.1 程式的驗證......................................27
3.1.1 一階Lagrange元素的驗證.....................27
3.1.2 二階Serendipity元素的驗證..................32
3.2 數值測試問題的說明..............................34
第四章 數值結果與討論..................................37
4.1 誤差的探討......................................37
4.2 求解時間的比較..................................46
4.3 新元素的優勢....................................54
4.4 超收斂點的位置..................................56
第五章 結論............................................58
參考文獻...............................................60
自述...................................................62
參考文獻 [1] D. L. Logon, “ A First Course in the Finite Element Method “, PWS-KENT, Boston, 1992.

[2] R. L. Taylor, P. J. Beresford, E. L. Wilson, “A non-conforming element for stress analysis”, International Journal for Numerical Methods in Engineering, Vol.10, 1211-1219, 1976.

[3] H. A. Taiebat, J. P. Carter, “Three-dimensional non-conforming elements”, Department of Civil Engineering Research Report R808, The university of Sydney, Australia, 2001.

[4] 蔡文傑, ”二維有限元素法之收斂性探討”, 國立成功大學機械工程研究所碩士論文, 2001.

[5] 林源富, ”運用高階有限元素解破裂點尖端應力強度因子”, 國立成功大學機械工程研究所碩士論文, 2002.

[6] 葉彥良, “特徵向量展開法與縮減矩陣法解多重負荷問題之探討” 國立成功大學機械工程研究所碩士論文, 2001.

[7] R. Barrett, M. Berry, T. F. Chan, J. Demmel, J. Dongarra, V. Eijkhout, R. Pozo, C. Rommel, H. van der Vorst, “Templates for the Solution of Linear System: Building Blocks for Iterative Method”, SIAM, 1994.

[8] 陳明凱, ”平行有限元素法之負載平衡探討”, 國立成功大學機械工程研究所碩士論文, 2001.

[9] J. N. Reddy, ”An Introduction to the Finite Element Method ”, 2nd edition, McGraw-Hill, Singapore, 1993.
[10] L. N. Trefethen, D. Bau, “Numerical Linear Algebra”, SIAM, USA, 1997.

[11] O. C. Zienkiewicz, R. L. Taylor, “The Finite Element Method”, 4th edition, McGraw-Hill, Singapore, 1989.

[12] H. Jean-Francois, B. Klaus-Jurgen, “On higher-order-accuracy points in isoparametric finite element analysis and an application to error assessment”, Computers and Structure 79, 1275-1285, 2001.

[13] A. P. Boresi, K. P. Chong, “Elasticity in Engineering Mechanics”, 2nd Edition, John Wiley & Sons, USA, 2000.

[14] D. S. Burnett, “Finite Element Analysis From Concepts to
Applications”, Addison-Wesley, Canada, 1987.

[15] H. T. Rathod, S. Kilari, “General complete Lagrange family for the cube in the finite element interpolations”, Computer Methods in Applied Mechanics and Engineering, 295-344, 2000.

------------------------------------------------------------------------ 第 3 筆 ---------------------------------------------------------------------
系統識別號 U0026-0812200910404666
論文名稱(中文) 螺旋齒輪減速機箱體結構電腦模擬分析及實驗
論文名稱(英文) The computer simulation and experiment of helical gear reducer box
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 陳源甫
學號 n1690430
學位類別 碩士
語文別 中文
口試日期 2003-07-09
論文頁數 64頁
口試委員 口試委員-褚晴暉
指導教授-何旭彬
口試委員-吳學鑑
關鍵字(中) 有限元素法
接觸效應
齒輪減速機
關鍵字(英) gear reducer
finite element method
contact effect
學科別分類
中文摘要 本文之目標在於探討如何利用有限元素法對齒輪減速機箱體結構進行適切的模擬分析,以預估箱體應力應變型態進而提供設計改良參考。
箱體結構本身形體複雜,在分析時需要做些簡化與假設以利電腦模擬的執行。首先以不含齒輪、傳動軸及軸承的齒輪減速機箱體來建立有限元素三維模型。只考慮靜態負荷。以靜力分析的方式將齒輪負荷分配到各軸承座,作為箱體模型的外力負荷,利用有限元素法模擬出箱體的應力應變分佈。同時對減速機箱體黏貼應變規進行實驗量測,以驗證電腦模擬的可靠度。
由於模擬與實驗兩者的結果比較後發現差距極大,考慮將傳動軸加入分析模型中作為分析修正,但模擬後卻發現結果相差更遠。探究原因為忽略了軸、軸承、箱體三者間的接觸效應,導致在接觸區的負荷情形產生偏差。
為了瞭解接觸效應對模擬的影響性,先對減速機中各軸局部進行簡單的二維接觸模式分析,由結果瞭解到接觸效應的特性以及先前模擬所存在的一些缺失。重新建立包含減速機箱體、傳動軸與軸承的有限元素三維接觸模型。同樣為靜態模擬,但此時的外力負荷則是以齒輪對傳動軸所造成的等效作用力為考量。
再次將模擬與實驗的結果做比較,發現大幅降低了兩者間的差距。所以三維接觸分析雖然複雜,但能有效改善模擬適切性,是較好的模擬分析方式。
英文摘要 The goal of this thesis is to set up a proper finite element model to simulate the gear reducer box. From the results of finite element simulation, we can estimate the state of stress and strain of the gear box and modify the design of the gear box.

Since the geometry of the gear box is complicated, some simplifications and assumptions are needed to do the finite element simulation. We start with the three dimensional finite model of the gear box which does not include the gears, shafts and bearings of the gear reducer. At first, we use static load instead of dynamic load. We use the gear load and the concept from statics to calculate the load act on the bearings and use the above results as the input to the finite element model.

Since there are big difference between the computer simulation results and experimental results, the finite element model must be improved. The gears, shafts and bearings are included in the second finite element model. But the difference between the simulation results and experimental results are bigger than before.

The contact effect between the shaft and the bearing must be included. A two dimensional simplified model is studied first, after we study the results from the two dimensional case, we simulate the three dimensional model. The results from the three dimensional model which include the gears, shafts, bearings and contact effect are very close to the results from the experiment.
論文目次 中文摘要................................................Ⅰ
英文摘要................................................Ⅱ
誌謝....................................................Ⅲ
目錄....................................................Ⅳ
表目錄..................................................Ⅶ
圖目錄..................................................Ⅷ
符號說明................................................Ⅹ

第一章 緒論.............................................1
1.1 研究動機與目的......................................1
1.2 研究流程與文章架構..................................2
第二章 相關理論.........................................7
2.1 有限元素法..........................................7
2.1.1 平衡方程式........................................7
2.1.2 線性應變與位移方程式..............................8
2.1.3 材料應力與應變關係式..............................8
2.1.4 最小位能原理......................................9
2.2 齒輪原理...........................................11
2.2.1 螺旋齒輪幾何性質.................................11
2.2.2 螺旋齒輪作用力分析...............................12
第三章 有限元素模型的建立..............................17
3.1 分析的螺旋齒輪減速機簡介...........................17
3.1.1 減速機的箱體構件.................................18
3.1.2 減速機的傳動機件.................................20
3.2 定義參考座標.......................................23
3.3 有限元素模型的建構.................................23
第四章 電腦模擬分析與實驗量測的步驟....................26
4.1 電腦模擬分析—不含軸的有限元素模型.................27
4.2 電腦模擬分析—含軸的有限元素模型...................37
4.2.1 含軸的有限元素模型—二維模擬.....................37
4.2.2 含軸的有限元素模型—三維模擬.....................40
4.3 實驗量測...........................................44
4.3.1 實驗目的.........................................44
4.3.2 實驗方法.........................................44
4.3.3 實驗裝置.........................................44
4.3.4 實驗流程.........................................46
第五章 電腦模擬與實驗量測結果之比較與討論..............48
5.1 實驗量測結果.......................................48
5.2 電腦模擬與實驗量測之結果比較.......................49
5.3 模擬差異性的探討...................................53
第六章 結論與建議......................................61
參考文獻...............................................63
自述...................................................64
參考文獻 參考文獻

[1] Robert L. Mott , Machine Elements in Mechanical Design , 2nd Edition , Prentice Hall , U.S.A , 1992 .

[2] 陳朝光,林守儀,盧燈茂,機械設計(二),高立圖書有限公司,台北,1991。

[3] COSMOS/WORKS version 7.0 User’s Guide , Structural Research and Analysis Corp. , U.S.A , 2001 .

[4] COSMOS/WORKS version 7.0 Tutorial , Structural Research and Analysis Corp. , USA , 2001 .

[5] 機械工程手冊/電機工程手冊編輯委員會,機械工程手冊3金屬材料,初版,五南圖書出版股份有限公司,台北,2002。

[6] 林樹均,葉均蔚,劉增豐,李勝隆,材料工程實驗與原理,全華科技圖書股份有限公司,台北,1992。

[7] 陳長有,許振聲,陳伯宜,機械工程實驗(Ⅰ)材料試驗,四版,全華科技圖書股份有限公司,台北,1990。

[8] 陳朝光,盧燈茂,機械設計(一),高立圖書有限公司,台北,1990。

------------------------------------------------------------------------ 第 4 筆 ---------------------------------------------------------------------
系統識別號 U0026-0812200910412780
論文名稱(中文) 高強度鋁合金冷鍛成形極限電腦輔助評估之研究
論文名稱(英文) Investigation on Computer-aided Evaluation of Forming Limit in Cold Forging of High Strength Aluminum Alloy
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 陳日興
學號 n1690160
學位類別 碩士
語文別 中文
口試日期 2003-07-14
論文頁數 86頁
口試委員 口試委員-李偉賢
口試委員-許光城
指導教授-李榮顯
關鍵字(中) 鍛粗
應變比值
延性破壞準則
有限元素法
應變路徑
破壞軌跡線
成形極限圖
冷鍛
高強度鋁合金
關鍵字(英) cold forging
strain ratio
upsetting
forming limit diagram
ductile fracture criterion
finite element method
strain path
high strength aluminum
fracture locus
學科別分類
中文摘要 為探討引發鍛粗製程( upsetting )之自由表面破壞的原因,本文從五種不同的角度觀點來評估五種延性破壞準則之製程適用性,並選用其中製程適用性最佳之準則來做為自由表面破壞之判斷依據,此五種觀點包括等效應力、最大拉張應力、最大拉張應力之正規化 ( normalize )、微觀空孔成長角度以及靜液壓應力等五種觀點。
文中吾人引用可成形性實驗所量測到的應變量,以適用性分析之方法,評估出最適合鍛粗製程的延性破壞準則後,再結合有限元素套裝軟體DEFORM-3D,針對高強度鋁合金Al-2017F進行圓柱壓縮模擬分析,預測Al-2017F在不同潤滑條件與胚料高度直徑比的成形極限。
本文成功的評估出Cockcroft and Latham延性破壞準則最適用於鍛粗製程之破壞預測,並利用該準則預測出Al-2017F在不同潤滑情況及胚料高度直徑比的成形極限。由模擬的結果顯示,摩擦係數與胚料高度直徑比並不會改變材料的破壞軌跡線,而實驗中途摩擦係數的變異,會導致應變路徑的改變,進而影響胚料的可成形性。透過本文的研究,未來僅需依製程特性選用適當的延性破壞準則,再透過有限元素法的模擬分析,最後只需做少數的實驗驗證,便可快速建立出材料完整的成形極限圖 ( FLD ),以提供製程或設計等相關人員在開發新產品或參數最佳化時,判斷胚料何時、何處破壞的依據。
英文摘要 To investigate the fracture on the free surface in upsetting process, five different ductile fracture criteria are evaluated in this research. The evaluated criteria include equivalent stress, maximum tensile stress, normalized maximum tensile stress, void growth and coalescence, and hydrostatic stress. After the most adoptable fracture criterion being obtained, we can identify the billet fractured or not by this criterion.
In this research, we used the limit strain data measured in the literature to evaluate the most adoptable fracture criterion. After the most adoptable fracture criterion being obtained, it is then used to create simulation model by the DEFORM-3D software to predict the forming limits under different process conditions. The simulation of cylinder compression for the Al-2017F alloy was performed in different friction conditions and height/diameter ratios.
The evaluated results show that the Cockcroft and Latham ductile fracture criterion is the most suitable for the fracture prediction in upsetting process. From the simulated results, friction coefficient and the height/diameter ratio will not change the fracture locus. The suddenly change of friction coefficient during experiments will affect the strain path, thus affecting the formability of the billet. With the proposed method, the construction of the forming limit diagram (FLD) can be simplified by selecting proper ductile fracture criteria during finite element simulation and comparing the simulated result with a few experimental results. Thus, the identification of fracture during process parameter optimization can be made.
論文目次 中文摘要........................................I
英文摘要........................................II
總目錄..........................................III
圖目錄..........................................VII
表目錄..........................................X
符號說明........................................XII

第一章 前言....................................1
1-1 緒論.......................................1
1-2 文獻回顧...................................3
1-3 本文研究範疇...............................12

第二章 金屬成形極限理論........................15
2-1 金屬成形概論...............................15
2-2 可鍛造性概論...............................16
2-3 整體成形之缺陷.............................17
2-4 延性破壞機制...............................18
2-5 成形極限圖概述.............................19
2-6 延性破壞準則之比較探討.....................23

第三章 電腦模擬分析............................27
3-1 有限元素法於塑性加工上之應用...............27
3-2 塑性成形之FEM力學模式分析..................28
3-3 DEFORM軟體簡介.............................32

第四章 實驗與模擬條件規劃......................35
4-1 實驗之條件規劃.............................35
4-1-1 圓環壓縮試驗之條件規劃...................35
4-1-2 圓柱壓縮試驗之條件規劃...................36
4-2 實驗之結果.................................38
4-2-1 各潤滑條件下的摩擦因子...................39
4-2-2 Al-2017F之塑流應力—應變圖...............39
4-2-3 各實驗規劃條件下的延性破壞點與應變路徑...40
4-3 圓柱壓縮有限元素模擬條件規劃...............41
4-3-1 CAD模型之建立............................41
4-3-2 參數之設定...............................44
4-4 網格佈建與點資料擷取.......................44
4-4-1 網格局部細化.............................44
4-4-2 點追蹤之位置.............................46
4-5 收斂性分析.................................47
4-6 模擬之假設模式.............................48

第五章 結果與討論..............................50
5-1 五種延性破壞準則之臨界破壞值與製程適用性分析...............................................50
5-1-1 五種延性破壞準則之臨界破壞值.............50
5-1-2 五種延性破壞準則之製程適用性分析.........54
5-1-3 製程特性對於延性破壞準則製程適用性之影響.57
5-2 應變路徑之探討.............................59
5-2-1 實驗與模擬應變路徑之比較.................59
5-2-2 摩擦係數對應變路徑之影響.................66
5-3 成形極限圖之探討...........................70
5-4 壓縮比與破壞應變之探討.....................71
5-4-1 壓縮比之探討.............................71
5-4-2 破壞應變之探討...........................73

第六章 結論與建議..............................76
6-1 本文結論...................................76
6-2 未來建議...................................77

附錄A 各應力、應變轉換成環向應變與軸向應變
關係式之計算式.................................79

附錄B 各延性破壞準則轉換成環向應變與軸向應變
關係式之計算式.................................81

參考文獻.......................................84
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1995
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1986
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Metalworking”, Academic Press, 1987
13.Frater, J. L. and B. R. Penza,“Predicting Fracture in Cold Upset Forging by
Finite Element Methods”, J. Materials Shaping Technology, vol. 7, pp.57-62,
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17.Jain, S.C. and S. Kobayashi,“Deformation and fracture of an aluminum alloy in
plain-strain side-pressing”, In Proc. 11th Int. MTDR Conf., pp.1137-1154, 1970
18.Ko, D. C., Byung-Min Kim and Jae-Chan Choi,“Prediction of surface-fracture
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------------------------------------------------------------------------ 第 5 筆 ---------------------------------------------------------------------
系統識別號 U0026-0812200910415963
論文名稱(中文) 小波有限元素法在旋轉葉片上的振動分析
論文名稱(英文) The Vibration Analyses of Rotary Blade by Using The Wavelets Finite Element Method
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 王中民
學號 n1690147
學位類別 碩士
語文別 中文
口試日期 2003-06-30
論文頁數 64頁
口試委員 指導教授-陳聯文
口試委員-賴新一
口試委員-許來興
關鍵字(中) 小波有限元素法
小波函數
關鍵字(英) wavelets function
wavelets finite element method
學科別分類
中文摘要 旋轉機械目前已成為機械技術領域中相當重要的一環,其中的設計問題又以旋轉葉片的振動分析最為關鍵。在傳統上,為了求得旋轉葉片的自然振動頻率,以有限元素法(finite element method)來作分析是常見的一種方式。
在有限元素法中,為求得更精確的解,可藉由提高單位元素的數目或者增加節點上的自由度來達成,但這會耗費許多計算上的時間。因此本文利用小波函數(wavelets)中的”尺度函數”(scalets),作為小波有限元素法中的內插形狀函數,小波係數作為單位元素自由度,再使用一空間轉換矩陣將小波空間中的自由度轉為實際的節點位移函數,並測試其在不同條件下的收斂性。
本文選擇Daubechies小波函數作為內插形狀函數,因其具有正交性、有限承載與良好的頻域及時域局部定位解析特性。由分析結果可以得知,小波有限元素法的確具有相當的可靠性及優異的收斂性,能減少計算時所需之單位元素數目,進而提高計算上的效率。
英文摘要 The rotary machines have been the important part of the mechanical technology fields. Among the design problems, the vibration analyses of the rotary blades are the key points. In order to get the natural frequencies of vibration, we usually use the finite element methods.
In the finite element method, we obtain the better solutions by increasing the element numbers, but this waste much time in computation. Therefore, we employ the “scalets” of the “wavelets” as the new interpolation functions, and the “wavelet coefficients” as the degrees of freedom. We must construct space transform matrix to transform the wavelet coefficients to nodal displacement functions. After all, their convergence in different conditions is tested.
Daubechies wavelets possess elegant properties of orthonormal, compact support and time-frequency localization. As the results, the wavelets finite element method has better convergence with less element numbers and improves the efficiency in calculation.
論文目次 摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 VI
圖目錄 VIII
符號說明 Ⅹ

第一章 緒論 1
1-1 前言 1
1-2 文獻回顧 2
1-3 論文大綱 4

第二章 小波理論 6
2-1 多層次解析之基本概念 6
2-2 Daubechies小波函數及尺度函數之計算 11
2-3 Daubechies小波之尺度函數微分值計算 14
2-4 尺度函數動量值 15
2-5 Daubechies小波之聯結係數 17

第三章 小波有限元素法 28
3-1 旋轉葉片的有限元素法分析 28
3-2旋轉葉片的小波有限元素法分析 33

第四章 結果與討論 42
4-1薄葉片的自然振動頻率分析結果 42
4-2結論 44

第五章 綜合結論與未來展望 57
5-1綜合結論 57
5-2未來展望 58

參考文獻 59

自述 64
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------------------------------------------------------------------------ 第 6 筆 ---------------------------------------------------------------------
系統識別號 U0026-0812200910423975
論文名稱(中文) 非均勻厚度壓電超音波換能器之分析模擬、製作與特性量測
論文名稱(英文) Simulation, Fabrication, and Characteristic Measurement of Piezoelectric Ultrasound Transducer with Non-uniform Thickness
校院名稱 成功大學
系所名稱(中) 機械工程學系碩博士班
系所名稱(英) Department of Mechanical Engineering
學年度 91
學期 2
出版年 92
研究生(中文) 李昆展
學號 n1690429
學位類別 碩士
語文別 中文
口試日期 2003-07-25
論文頁數 107頁
口試委員 口試委員-朱聖緣
口試委員-羅如燕
口試委員-楊旭光
指導教授-李永春
關鍵字(中) 壓電陶瓷
等效電路
非均勻厚度
有限元素法
超聲波換能器
非破壞性檢測
關鍵字(英) equivalent circuit
piezoelectric ceramic
non-destructive evaluation
non-uniformthickness
ultrasound transducer
finite element method
學科別分類
中文摘要   本論文研究自製之非均勻厚度PZT壓電陶瓷體,與其所製成的聚焦式超聲波換能器;研究範圍包括理論模擬、製程實作、與實驗量測。
  在理論方面採用有限元素法及等效電路模型二種方法。首先利用ANSYS有限元素法軟體進行阻抗分析,再與PSpice軟體之等效電路模擬結果作比對。Spice等效電路模型方面,採用A. Püttmer等效電路模型,將壓電材料分成聲學介質與電路端兩個部分,分別可用傳輸線與電容代替,再加上控制源估計機電轉換效應;同時參考G. Lypacewicz之Mason等效電路模型,完成非均勻厚度壓電陶瓷體等效電路模型。在製程實作與實驗量測方面,首先於實驗室中製作均勻厚度與非均勻厚度的壓電陶瓷體,以阻抗分析儀量測其頻率響應,並與模擬的結果作比對;接著以自製之壓電陶瓷體,設計製作出點聚焦的超聲波換能器,並結合聲場掃瞄系統與水聽器,以了解自製換能器的性能。實驗結果發現具有銅背層的非均勻壓電體換能器,確實能增加換能器頻寬。
  經由本文之實驗與模擬分析,證明非均勻厚度壓電陶瓷體等效電路的可行性,可以作為設計壓電超音波換能器的的依據,未來可以設計出頻寬更寬、中心頻率更高的超音波換能器,作為非破壞性檢測的應用。
英文摘要   This research investigates the focusing acoustic wave transducers, which are made from PZT piezoelectric ceramic with non-uniform thickness, and their performance. The investigation covers theoretical simulation, fabrication, and experimental measurement.
  The simulation is based on finite element method (FEM) and equivalent circuit model. The piezoelectric impedance analysis has been carried out with ANSYS FEM analysis and PSpice equivalent circuit simulation. The equivalent circuit model of piezoelectric material is based on A. Püttmer’s work (1997), which consists of two parts, namely acoustic part and electric part. Both parts can be substituted by transmission lines and capacitors. Using an improve model proposed by G. Lypacewics (2002), the characteristics of a piezoelectric ceramic with non-uniform thickness is studied. The uniform and non-uniform piezoelectric ceramic disks are fabricated and measured by an impedance analyzer. The acoustic wave transducers are fabricated by those ceramics. The transducers’ properties are investigated with an acoustic field scanning system. It shows that the bandwidth of the transducer is improved with non-uniform thickness and proper backing material.
  The experimental and simulation results of this work pave a way for designing a focusing ultrasound transducer with non-uniform thickness PZT ceramics. With wider bandwidth and higher central frequency, such transducer can be very useful for future non-destructive evaluation (NDE).
論文目次 摘要 ………………………………………………………………………… I
Abstract …………………………………………………………………… II
致謝 ………………………………………………………………………… III
目錄 ………………………………………………………………………… IV
表目錄 ……………………………………………………………………… VII
圖目錄 ……………………………………………………………………… VIII
符號說明 …………………………………………………………………… XIII

第一章 導論 ………………………………………………………………… 1
1-1 研究背景與目的 …………………………………………………… 1
1-2 文獻回顧 …………………………………………………………… 2
1-3 本文架構 …………………………………………………………… 4
第二章 理論基礎 …………………………………………………………… 5
2-1 彈性波在等向性及非等向性材料中的傳播行為…………………… 5
2-1-1 彈性波在等向性材料中的傳播行為 ……………………………… 7
2-1-2 彈性波在非等向性材料中的傳播行為……………………………… 8
2-2 壓電特性及壓電陶瓷之應用………………………………………… 9
2-2-1 壓電統御方程式……………………………………………………… 10
2-2-2 壓電材料重要參數…………………………………………………… 11
2-2-3 PZT壓電陶瓷的材料特性…………………………………………… 13
2-2-4 PZT超聲波換能器…………………………………………………… 14
2-3 彈性波在壓電材料中的傳播………………………………………… 15
2-4 壓電材料的等效電路………………………………………………… 17
2-4-1 等向性材料一維波傳等效模型……………………………………… 17
2-4-2 壓電材料的類比模型………………………………………………… 22
第三章 模擬 ………………………………………………………………… 28
3-1 ANSYS 模擬…………………………………………………………… 28
3-1-1 有限元素法簡介……………………………………………………… 28
3-1-2 ANSYS模擬壓電換能器……………………………………………… 29
3-2 PSpice模擬…………………………………………………………… 33
3-2-1 均勻厚度壓電片PSpice模擬………………………………………… 33
3-2-2 非均勻厚度壓電片PSpice模擬……………………………………… 37
3-3 ANSYS與PSpice模擬壓電圓盤之比較………………………………… 41
第四章 實驗與量測 …………………………………………………………… 46
4-1 PZT換能器製作………………………………………………………… 46
4-1-1 PZT壓電陶瓷製作……………………………………………………… 46
4-1-2 換能器製作……………………………………………………………… 61
4-2 PZT換能器特性量測…………………………………………………… 63
4-2-1 PZT基本特性量測……………………………………………………… 63
4-2-2 自製換能器基本特性量測……………………………………………… 73
第五章 量測結果與模擬分析 ………………………………………………… 83
5-1 自製PZT試件及換能器與模擬比較…………………………………… 83
5-1-1 自製PZT模擬…………………………………………………………… 83
5-1-2 自製PZT換能器模擬…………………………………………………… 86
5-2 平板型與非均勻厚度型換能器特性比較……………………………… 89
第六章 結論 …………………………………………………………………… 99
6-1 結論 …………………………………………………………………… 99
6-2 未來展望 ……………………………………………………………… 101
參考文獻 …………………………………………………………………………… 102
附錄A 等向性材料一維波傳等效電路………………………………………… 105
附錄B 壓電材料一維波傳等效電路……………………………………………… 106
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