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研究生：	蘇哲民 Sue, Che-ming
論文名稱：	雙層功能梯度中空圓柱或圓盤之數值解 Numerical Analysis of Compound Cylinders or Disks with Functionaly Graded Materials
指導教授：	褚晴暉 Chue, Ching-Hwei
學位類別：	碩士 Master
系所名稱：	工學院 - 機械工程學系 Department of Mechanical Engineering
論文出版年：	2010
畢業學年度：	98
語文別：	中文
論文頁數：	80
中文關鍵詞：	功能梯度材料、中空圓盤、複合圓柱、中空圓柱
外文關鍵詞：	hollow disks, functional graded material, hollow cylinders, compound cylinders
相關次數：	點閱：152 下載：2
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查詢本校圖書館目錄查詢臺灣博碩士論文知識加值系統勘誤回報

本論文以多層均質材料，模擬楊氏係數與密度沿著徑向方向呈冪次
方函數變化的功能梯度材料。主要目的為使用有限元素軟體來求解功能梯度中空圓盤或圓柱之應力場及位移場。並把數值解與公式解進行比較及討論。以單層中空圓盤而言分別探討承受內壓、外壓、旋轉時之應力場與位移場。而單層中空圓柱則針對受到溫度和應力負載，討論其應力場與位移場。雙層中空圓盤則討論內外圓盤間，存在干涉量時之應力場及求解內外圓盤不發生鬆脫的臨界角速度。

This thesis studies the finite element solutions of the displacement and stress fields of functionally graded hollow disks or cylinders subjected to mechanical and thermal loads. The numerical results are then compared with
the existing analytical solutions. In these closed form solutions, the material properties such as the Young’s modulus, density and the coefficient of thermal expansion are assumed to vary in a power law, while the Poisson’s ratio is kept as a constant. In the numerical calculation, the functionally graded material is simulated by several layers. The material of each layer is homogeneous and varies with the same power form as that of functionally
graded disks or cylinders. Several examples are demonstrated to show the possibility of finite element simulation for non-homogenous structures.

摘要 ...................................................I
Abstract ...............................................II
誌謝 ...................................................III
目錄 ....................................................IV
表目錄...................................................VI
圖目錄 .................................................VII
符號說明 ................................................IX
第一章 緒論 ..............................................1
1-1 前言..................................................1
1-2 文獻回顧............................................. 4
1-3 研究動機............................................. 6
1-4 本文架構 ............................................ 7
第二章 基礎理論與分析方法 ................................8
2-1 彈性力學基本方程式................................... 8
2-2 二維問題............................................ 10
2-2.1 平面應力...........................................10
2-2.2 平面應變 ......................................... 11
2-2.3 軸對稱 ........................................... 13
2-3 有限元素分析 ....................................... 14
第三章 單雙層功能梯度中空圓盤或圓柱之有限元素模型........18
3-1 受內外壓之單層中空圓盤.............................. 19
3-2 受旋轉之單層中空圓盤 ............................... 20
3-3 受內壓及溫度之單層中空圓柱 ......................... 21
3-4 雙層中空圓盤 ....................................... 22
第四章 單雙層功能梯度中空圓盤或圓柱結果與討論 ...........24
4-1 單層功能梯度中空圓盤或圓柱之結果與討論 ............. 24
4-1.1 受內壓之單層中空圓盤 ..............................26
4-1.2 受外壓之單層中空圓盤 ............................. 36
4-1.3 受旋轉之單層中空圓盤 ..............................43
4-1.4 受內壓及溫度之單層中空圓柱.........................52
4-2 雙層中空圓盤之結果與討論 ........................... 60
4-2.1 無外加負載之雙層中空圓盤 ..........................62
4-2.2 雙層中空圓盤之旋轉問題 ........................... 74
第五章 結論 .............................................75
參考文獻 ................................................78
附錄一. .................................................80
                                    

Horgan, C. O. and Chan, A. M., The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials. Journal of Elasticity 55, 43-59, 1999.
Jabbari, M. Sohrabpour, S. and Eslami, M. R., Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. International Journal of Pressure Vessels and Piping 79, 493-497, 2002.
Nejad, M. Z. and Rahimi, G. H., Deformations and stresses in rotating cylindrical pressure vessels of functionally graded materials. Journal of Elasticity 55, 43-59, 1999.
Tutuncu, N. and Ozturk, M., Exact solutions for stresses in functionally graded pressure vessels. Composite: Part B 32, 683-686, 2001.
Tutuncu, N., Stresses in thick-walled FGM cylinders with exponentially varying properties. Engineering Structures 29, 2032–2035, 2007.
Zenkour, A., Analytical solutions for rotating exponentially-graded annular disks with various boundary conditions. International Journal of Structural Stability and Dynamics 5, 557–577, 2005.
Zenkour, A., Steady-state thermoelastic analysis of a functionally graded rotating annular disk. International Journal of Structural Stability and Dynamics 6, 559–574, 2006.
卓建佑，雙層功能梯度中空圓盤或圓柱之應力解析解Exact solutions for stresses in double-layered functionally graded hollow discs or cylinders，國立成功大學論文，台南市，2008。
劉晉奇，褚晴暉，有限元素分析與ANSYS 的工程應用。滄海書局，2006。

校內：立即公開
校外：2009-10-21公開

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