臺灣博碩士論文加值系統

本文應用移動最小二乘法(Moving Least Square Method, MLSM)分析Mindlin平板問題。本方法之特點為利用移動最小二乘法建立局部近似函數，在建立同時加入限制條件，使其滿足微分方程式及邊界條件。考慮節點上函數之殘值，建立殘值二次式，並加上限制條件，令為目標函數，由目標函數之最小化，得到以節點上函數值表示之近似函數。利用各節點函數值之一致條件以置點法可建立聯立方程式並求解。數值範例中，分析不同載重、作用力及邊界條件下板的變位、轉角、彎矩和剪力，並與解析解比較檢驗其誤差及收斂率。

In this thesis, the moving least square method is used to analyze the mechanical problems of Mindlin plates. The novelty of this approach is that, we add constraint into the moving least square approach to establish the approximate function, so that it satisfies both the differential equation and boundary conditions.
In numerical examples, we analyze the problem to obtain the deflection, rotation, bending moment and shear force of the plates under different loads and boundary conditions, and compare the numerical results with the exact solution to examine the accuracy and the rate of convergence .

摘要 I
Abstract II
致謝 III
目錄 IV
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1前言 1
1.2無元素法的發展 2
1.3 本文架構 3
第二章 控制方程式推導 5
2.1 一階剪應變形平板理論 5
2.2 邊界條件 9
2.3 四邊簡支承板受雙正弦載重之解析解 10
2.4多項式解析解 11
第三章 移動最小二乘法之應用 23
3.1 移動最小二乘法 23
3.2 限制條件為微分方程式之最小二乘法 24
3.3 支撐半徑與加權之選取 26
第四章 數值範例分析結果 27
4.1四邊簡支承板受雙正弦載重 27
4.2 多項式解析解比較 28
4.2.1 平板受線性剪力與彎矩為主的作用力 28
4.2.2 平板受線性剪力與彎矩為主的作用力 29
4.2.3 平板受線性荷重與x向剪力為主的作用力 29
4.2.4 平板受二次荷重與x向剪力為主的作用力 30
第五章 結論 32
參考文獻 33

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