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研究生:許昆中
研究生(外文):Kun-ChungHsu
論文名稱:三維高階界面應力在結構力學基礎課題之探討
論文名稱(外文):Some aspects on the mechanical behavior of high-order surface/interface stresses in three-dimensional configurations
指導教授:陳東陽陳東陽引用關係
指導教授(外文):Tung-Yang Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:119
中文關鍵詞:高階表面/界面應力能量法
外文關鍵詞:high-order surface/interface stressesenergy approachmodified Stoney formula
相關次數:
  • 被引用被引用:1
  • 點閱點閱:343
  • 評分評分:
  • 下載下載:19
  • 收藏至我的研究室書目清單書目收藏:0
隨著科技與奈米製程的進步,當物體尺度越縮越小時,其表面積對體積之比率將會增大,此時界面/表面應力的效應對整體結構力學行為之影響將不可忽略。本文將在古典力學的架構下,基於Kirchhoff-Love的應變假設模擬出高階界面應力效應,並探討界面的軟硬程度將界面應力條件分類。另外以能量法與變分理論,推導出球形內含物複合材料系統在不同變形模式下的高階界面應力關係式。最後於古典Stoney formula之理論下,在薄膜/基板系統中模擬高階界面應力效應,並重新檢視與推導出修正公式。

When the size of solids or structures is in the nanometer scale, the effect of surface/interface stresses on the overall mechanical behavior cannot be ignored. Based on the kinematic deformation of Kirchhoff-Love assumption for the interphase between two neighboring media, we have modeled the high-order interface stresses effects in three-dimensional Cartesian coordinate system. Depending on the difference in stiffness and length scales of the interphase, it is shown that the interface conditions can be classified into several different types. Additionally, by using variation approach, high-order interface conditions were derived for composite with spherical inclusions under different deformation modes. To illustrate the high-order effect of interface stress in the thin film/substrate system, we also refine the Stoney formula and provide a modified formulation.
摘要 I
Abstract II
誌謝 III
目錄 IV
圖目錄 VI
表目錄 VII
第一章 緒論 1
1.1 文獻回顧與研究動機 1
1.2 論文架構與內容介紹 4
第二章 直角坐標系統下高階界面效應之探討 5
2.1 三維直角座標下之固體界面行為 5
2.2 三維直角坐標之界面基本關係式 17
2.3 三維直角座標高階界面效應之order探討 21
2.4 二維直角座標高階界面效應之order探討 42
第三章 球形內含物的高階界面效應 50
3.1 推導程序 50
3.2 基本方程式 52
3.2.1 基質與球形內含物的基本方程式 52
3.2.2 界面基本方程式 53
3.3 球形內含物對稱變形的高階界面效應 56
3.3.1 基質與內含物的位移控制方程式 56
3.3.2 界面處的界面效應 61
3.4 球形內含物剪力變形的高階界面效應 66
3.4.1 基質與內含物的位移控制方程式 66
3.4.2 界面處的高階表面效應 72
第四章 薄膜/基板系統之高階界面應力效應探討 88
4.1 古典Stoney formula之基本理論 89
4.2 考慮高階界面應力效應之Modified Stoney formula 94
第五章 結論與未來展望 101
5.1 結論 101
5.2 未來展望 101
參考文獻 104
附錄A:界面材料參數之比較 109
附錄B:廣義正交曲線座標與變分結果之對照與驗證 112

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