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研究生： 陳彥吉
Yen-chi Chen
論文名稱： 功能梯度材料圓形板受側向載重之力學分析
Mechanical Analysis of circular Functionally Graded Materials plate subjected to transverse loads
指導教授： 張燕玲
Yen-Ling Chung
口試委員: 鄭蘩
Van Jeng
黃慶東
Ching-Tung Huang
學位類別： 碩士
Master
系所名稱： 工程學院 - 營建工程系
Department of Civil and Construction Engineering
論文出版年： 2006
畢業學年度： 94
語文別： 中文
論文頁數： 141
中文關鍵詞： 功能梯度材料
外文關鍵詞： Functionally Graded Materials
相關次數： 點閱：146  下載：3 
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    • 本研究主要是在分析圓形功能梯度板在固定端與簡支端之束制下受均佈載重作用之力學分析。首先依照彈性力學之基礎與板殼元素之理論先建立功能梯度材料圓形板之應變與位移的關係，並且求得應力場，包括軸力、剪力與彎矩，依此以獲得圓形板之控制方程式，並可求得圓形之理論解，在理論解中包括齊性解與特解，先依照控制方程式以求得齊性解，再依照不同之邊界條件獲得固定端與簡支端之特解。

    其次依照理論解中所要求之圓板尺寸建立有限元素之模型，並且考慮三種材料性質，分別為幕次方函數型(P-FGM)、S型函數(S-FGM)與指數函數型(E-FGM)，以有限元素法計算其數值解，藉此以驗證理論解之正確性。

    由比較後之結果顯示，理論解與數值解之誤差皆小於5%，因此，本篇論文之理論解將可適用於邊界條件與本論文所提出之相同條件下的情形。

    The main purpose of this research is to analyze the mechanics behavior of circular Functionally Graded Materials (FGM) plate with damped edge and simply supported subjected to uniform load. First, based on the theory of elasticity and the classical plate theory, the governing equation are determined by deriving the relation among strain deflection and stress field, including axial force, shear force, and moment. Consequently, the theoretical solutions will be derived by solving governing equations for different boundary conditions. Second, for circular plates with Young’s modulus distributes in thickness direction obeying power-law function (simply called P-FGM), sigmoid function (S-FGM), and exponential function (E-FGM), the finite element mesh of circular plates is set up to obtain numerical solutions. Finally, the numerical computation obtained by FGM will be compared with theoretical solutions to examine the accuracy of the results. The results reveal that the theoretical solutions are available for case whose conditions are the same as that of this thesis.

    第一章 序論………………………………………………………………………1 1.1 研究動機與目的…………………………………………………………1 1.2 文獻回顧…………………………………………………………………1 1.3 研究內容…………………………………………………………………6 第二章 功能梯度材料圓形板之理論基礎………………………………9 2.1 FGM圓板之基本理論………………………………………………...…9 2.2 FGM圓板之應變及位移關係………………………………………...…10 2.3 FGM圓板之應力場……………………………………………….......…11 2.4 平衡方程式……………………………………………….......………….15 2.5 中性面之位置…………………………………………….......………….18 2.6 結論……………………………………………………….......………….19 第三章 功能梯度材料板之理論解…………………………………………21 3.1 位移函數之齊性解……………………………………….......………….21 3.2 位移函數之特解……………………………………….......…………….23 3.3 FGM之材料性質……………………………………….......……………24 3.3.1 幕次方函數型(P-FGM) ……………………….......……….……24 3.3.2 S型函數(S-FGM) ……………………….......………………..…26 3.3.3 指數函數型(E-FGM) …………………….......………………….27 3.4 結論……………………………………………………….......………….28 第四章 邊界為固定端受均佈載重下之FGM圓板的力學分析………29 4.1 理論推導………………………………………………….......………….29 4.2 有限元素之數值分析………………………………….......…………….32 4.2.1 幕次方函數型FGM(P-FGM)圓板之有限元素分析……………34 4.2.2 S-FGM圓板之有限元素分析……………….......……………....53 4.2.3 E-FGM圓板之有限元素分析……………….......……………....72 4.2.4 P-FGM、S-FGM與E-FGM板之力學行為比較……………........80 第五章 邊界為簡支端受均佈載重下之FGM圓板的力學分析……....83 5.1 理論推導………………………………………………….......………….83 5.2 有限元素之數值分析………………………………….......…………….85 5.2.1 幕次方函數型FGM(P-FGM)圓板之有限元素分析……………86 5.2.2 S-FGM圓板之有限元素分析……………….......……………..104 5.2.3 E-FGM圓板之有限元素分析……………….......……………..123 5.2.4 P-FGM、S-FGM與E-FGM圓板之力學行為比較……………..131 第六章 結論與建議…………………………………………………………133 6.1 結論……………………………………………………….......………133 6.2 建議……………………………………………………….......………134 參考文獻……………………………………………………….......……………137

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