臺灣博碩士論文加值系統

本文主要以等效均質梁理論，將內部材料視為一函數分佈之FGM板，利用等效均質梁理論建立與FGM板材料係數C11之關係，進行FGM板的等效均質化分析。使用三種材料分佈形式，冪次方函數(P-FGM)、S型函數(S-FGM)及指數型函數(E-FGM)之FGM板，楊氏模數分佈為使用內部為等效均質之等效楊氏模數概念，分別建立兩種不同邊界條件: (1) x向對邊為簡支端、y向對邊為自由端，(2) x向對邊為簡支端、y向對邊為固定端，進而代入y向邊界條件得其挫屈載重。此外，將FGM板等效均質化概念延伸至FGM濺鍍板及FGM介面塗層板挫屈行為，以有限元素軟體MARC分析等效均質板數值解。為證明等效均質板所得之挫屈載重正確性，將數值分析結果與鄭羽婷[32]之研究進行相互交叉比對，探討不同材料指數、彈性支承勁度、邊界條件…等參數下對挫屈載重的影響。研究結果顯示，楊氏模數分佈為函數變化及常數所分析之挫屈載重皆近似，挫屈載重間相關係數達0.9999；而固定材料指數及楊氏模數比時，改變材料分佈對挫屈載重影響劇烈；邊界條件對板的束制能力越佳，則挫屈強度越高；彈性支承的增加有助於提高整體挫屈強度；在三種不同板種類及材料分佈型式中，S-FGM濺鍍板抵抗挫屈能力最佳。

The main purpose of this article is utilizing Equivalent Homogeneous Beam Theory to analyze the buckling behavior of FGM rectangular plates with uniform elastic support under axial load. Using Equivalent Homogeneous Beam Theory to establish the relationship between material coefficient C11 to analyze the equivalent homogeneous results of FGM plates. The research is concentrated on three kinds of material distribution type which are power-law function (P-FGM), sigmoid function (S-FGM) and exponential function (E-FGM). Two kinds of boundary conditions are considered. One is simply-support at the opposite of x-axis, the others is simply-support at the x-axis with fixed end at the opposite of y axis. Moreover, extending the concept of equivalent homogeneous to FGM coated plates and FGM undercoated plates and calculated by finite element method using MARC program. To prove the accuracy of solution, compare the results with FGM plates and FGM theory value which was researched by Yu-Ting Cheng[32]. Discuss the behavior of buckling load under different kinds of parameters such as material index, stiffness of elastic support…etc. The result shows that buckling load will change seriously under same material index and Young’s modulus, equivalent homogeneous plates behave same as functionally graded material plates, increasing stiffness of elastic support could improve the buckling load of all structure and S-FGM coated plates is the best material to resist the buckling load under three kinds of material distribution and plate type.

目錄 III
圖索引 VIII
表索引 XXI
第一章 緒論 1
1.1 研究動機與目的 1
1.2 文獻回顧 2
第二章 等效均質板之理論基礎 10
2.1 等效均質梁 10
2.1.1 基本假設 10
2.1.2 FGM梁理論 10
2.1.3 等效均質梁理論 11
2.2 FGM板等效均質化 12
2.2.1 FGM板材料分佈 12
2.2.2 等效均質板(Equivalent Homogeneous Plate，簡稱EH plate) 12
2.3 等效均質板材料分佈形式 13
2.3.1 等效楊氏模數P-FGM板 14
2.3.2 等效楊氏模數S-FGM板 15
2.3.3 等效楊氏模數E-FGM板 16
第三章 FGM板的挫屈載重 19
3.1 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為自由端之挫屈分析 19
3.1.1 均佈彈性支承FGM板在x向對邊為簡支端、y向對邊為自由端之理論解 19
3.1.2 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為自由端之有限元素分析模擬 21
3.1.3 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為自由端之理論解與數值解的比較 22
3.2 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為固定端之挫屈分析 30
3.2.1 均佈彈性支承FGM板在x向對邊為簡支端、y向對邊為固定端之理論解 30
3.2.2 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為固定端之有限元素分析模擬 31
3.2.3 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為固定端之理論解與數值解的比較 33
3.3 均佈彈性支承FGM等效均質板在不同彈性勁度下挫屈載重比較 40
第四章 FGM濺鍍板的挫屈載重 44
4.1 FGM濺鍍板及等效均質板材料分佈 44
4.1.1 P-FGM濺鍍板之等效楊氏模數 45
4.1.2 S-FGM濺鍍板之等效楊氏模數 46
4.1.3 E-FGM濺鍍板之等效楊氏模數 48
4.2 均佈彈性支承FGM等效均質板在x向對邊為簡支端、y向對邊為自由端之挫屈分析 51
4.2.1 均佈彈性支承FGM濺鍍板在x向對邊為簡支端、y向對邊為自由端之理論解 51
4.2.2 均佈彈性支承FGM等效均質濺鍍板在x向對邊為簡支端、y向對邊為自由端之有限元素分析模擬 52
4.2.3 均佈彈性支承FGM等效均質濺鍍板在x向對邊為簡支端、y向對邊為自由端之理論解與數值解的比較 52
4.3 均佈彈性支承FGM等效均質濺鍍板在x向對邊為簡支端、y向對邊為固定端之挫屈分析 59
4.3.1 均佈彈性支承FGM濺鍍板在x向對邊為簡支端、y向對邊為固定端之理論解 59
4.3.2 均佈彈性支承FGM等效均質濺鍍板在x向對邊為簡支端、y向對邊為固定端之有限元素分析模擬 60
4.3.3 均佈彈性支承FGM等效均質濺鍍板在x向對邊為簡支端、y向對邊為固定端之理論解與數值解的比較 60
第五章 FGM介面塗層板的挫屈載重 67
5.1 FGM介面塗層板材料性質分佈 67
5.1.1 P-FGM介面塗層板 68
5.1.2 S-FGM介面塗層板 70
5.1.3 E-FGM介面塗層板 71
5.2 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為自由端之挫屈分析 74
5.2.1 均佈彈性支承FGM介面塗層板在x向對邊為簡支端、y向對邊為自由端之理論解 74
5.2.2 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為自由端之有限元素分析模擬 75
5.2.3 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為自由端之理論解與數值解的比較 75
5.3 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為固定端之挫屈分析 82
5.3.1 均佈彈性支承FGM介面塗層板在x向對邊為簡支端、y向對邊為固定端之理論解 82
5.3.2 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為固定端之有限元素分析模擬 83
5.3.3 均佈彈性支承FGM等效均質介面塗層板在x向對邊為簡支端、y向對邊為固定端之理論解與數值解的比較 83
第六章 綜合比較與探討 90
6.1 FGM板、FGM濺鍍板及FGM介面塗層板比較 90
6.2 P-FGM板、S-FGM板及E-FGM板比較 92
6.3 FGM板與等效均質板比較 94
6.4 不同邊界條件之FGM板比較 97
第七章 結論與建議 100
7.1 結論 100
7.2 建議 102

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