臺灣博碩士論文加值系統

本文應用移動最小功法(Moving Least Work method, MLW)對Mindlin平板問題進行數值模擬。本方法之特點為利用移動最小功法建立局部近似函數，在進行加權殘值方法時，其中是以殘值量乘以權函數再乘上其共軛的殘值量，使其含最小功的概念在其中，最後以置點的方式求解得到位移場和合應力場。
文中模擬了四邊簡支承平板承受雙正弦載重及多項式解析解引申出平板的邊界值問題，經由不同的基底階數和改變均勻佈點的數目去比較解析解以驗證移動最小功法的可行性，並分析其各變量最大值精度及誤差收斂的情形。

In this thesis, the Moving Least Work (MLW) method is used to model the mechanical behaviors of Mindlin Plates. This method uses the Moving Least Work approach to establish approximating functions. In the weight-residual problem precess, the residual value is multiplied by the weight function and multiplied by the conjugate residual value, so that it contains the conception of the least work. Finally we used the point collocation method to get the solutions of displacement fields and stress resultant fields.
The simply supported Mindlin plate is modeled under the sinusoidal load, and the boundary-value problems are solved by polynomial-analytic solutions. Using different basis functions and changing the numbers of the uniform-distributed points, we compared the numerical solutions with analytic solutions to validate the feasibility and convergence of the present method.

摘要 I
Abstract II
致謝 VIII
目錄 IX
表目錄 XI
圖目錄 XII
第一章 緒論 1
1.1 前言 1
1.2 文獻回顧 2
1.3 本文架構 4
第二章 Mindlin平板理論 5
2.1 控制方程式 5
2.2 邊界條件 9
2.3 四邊簡支端平板解析解 11
2.4多項式解析解 13
第三章 移動最小功法理論 27
3.1 移動最小功法 27
3.2 基底函數 29
3.3 鄰近點數目與影響半徑 30
3.4 權重函數 30
3.5 均方根誤差 31
第四章 數值範例 32
4.1 四邊簡支端平板承受雙正弦載重 32
4.2 多項式解析解與數值解比較 33
4.2.1 平板主要承受均布荷重 33
4.2.2 平板主要承受線性荷重 33
4.2.3 平板主要承受線性荷重且在x=a處承受x向彎矩與x向橫向剪力作用 35
4.2.4 平板主要承受二次非線性荷重 36
4.2.5 平板主要承受二次非線性荷重與在"x=a" 處承受"x" 向彎矩與"x" 向橫向剪力作用 37
第五章 結論 38
參考文獻 39

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