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研究生： 王何維
Wang, Ho-wei
論文名稱： 邊界條件為非線性之板的靜態分析
Static Deflection of a Plate with Nonlinear Elastic Supports
指導教授： 李森墉
Lee, Sen-Yung
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： 2009
畢業學年度： 97
語文別： 中文
論文頁數： 79
中文關鍵詞： Shifting Method 、Balance Method 、靜態 、移位函數 、非線性邊界 、板 、Kirchhoff
外文關鍵詞： deflection, static, nonlinear boundary, plate, Shifting Method, Balance Method
相關次數： 點閱：145  下載：1 
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    • 本篇論文主要探討古典Kirchhoff 板具有非線性邊界的靜態問題。在
    文中使用Balance Method 對原統御方程式與邊界條件做處理，之後則使用Shifting Method 處理非線性邊界，最後我們可以發現對於此類非線性邊界的靜態問題只需利用Shifting Method 就可得出解答，且可是用於強、弱非線性邊界。此外本文也有探討對於不同個數的模態假設之下之結果的精確程度，探討其收斂行為。

    This literary has studied static deflection of Kirchhoff plate with
    nonlinear elastic boundary conditions. Balance Method is the first step to modify governing equation and boundary condition into single parameter form. Then using Shifting Method solve static plate deflection problem with nonlinear boundary. We assume more than one mode into the equations, and further, discussing the numerical results with one mode assumption.
    In the end, these problems with nonlinear boundary condition can be solved by Shifting Method.

    摘 要 I Abstract II 誌　　謝 III 目 錄 IV 表 目 錄 VI 圖 目 錄 VII 符 號 XI 第一章 緒 論 1 1.1 前 言 1 1.2 文獻回顧 1 1.3 研究動機與方向 3 第二章 非線性邊界之Kirchhoff板之靜態分析 5 2.1 無因次化之統御方程式與邊界條件 5 2.2 Balance Method配合變數變換法求解 6 2.2.1 Balance Method介紹 6 2.2.2 問題描述與求解 7 2.3 移位函數與轉移函數之求解 10 2.3.1 移位函數與轉移函數滿足之條件 10 2.3.2 移位函數與轉移函數之解 11 2.3.3 組合移位函數與轉移函數之解 13 第三章 板之數值分析與討論 15 3.1 一端具非線性邊界之薄板分析 15 3.2 一端具非線性扭轉彈簧邊界之薄板分析 23 3.3 兩端皆具非線性邊界之薄板分析 28 第四章 板之進階數值分析與討論 35 4.1 邊界條件為 P-C-P-nK 的進階模型修正 35 4.2 邊界條件為 P-C-P-RnK 的進階模型修正 48 4.3 邊界條件為 P-nK-P-nK 的進階模型修正 53 4.4 邊界條件為P-C-P-nK與P-C-P-Rnk與P-nK-P-nK 的進階模型數值討論 58 第五章 結論 74 參考文獻 76 自述 79

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