臺灣博碩士論文加值系統

本文以受束制之移動最小二乘法分析古典板問題，此方法特點為，在以移動最小二乘法建立局部近似函數同時加入限制條件，使其滿足對應之控制方程式及邊界條件。古典板控制方程式為四階微分方程式，分析此類高階微分方程式問題時，採用Hermite型式之近似法，將函數之殘值及其一階導數之殘值皆納入殘值二次式考慮，使節點上之殘值最小化，得到以節點上函數值及其一階導數表示之近似函數，利用各節點函數值之一致性條件，以置點法建立聯立方程式求解。
數值算例中，分析受各種形式之載重和邊界條件之平板，以本文方法求得其位移、轉角、彎矩、剪力，並與解析解相比較，討論其精度和收斂性。

This thesis presents a constrained moving least square method to solve the problems of the classical plate. The novelty of this approach is that, constraints are added to make the approximate function satisfy the governing equation and boundary conditions while the approximate function is established by the moving least square approach. To analyze the problems of the high order differential equation, such as classic plates, we attempt to reduce the weighted sum of the residuals that results from the approximation to the field variable and its first derivatives. The process leads to an interpolation function which is express in terms of the nodal values of the field variable and its first derivatives. According to the requirement of the consistency of the interpolation function with its value at nodes, the point collocation technique was employed to determine the unknown nodal values, and the approximation solution can thus be found.
Various examples for the plate under different loads and different boundary conditions are solved to examine the accuracy and the rate of convergency of this method.

目錄
摘要 I
Abstract II
誌謝 III
目錄 V
表目錄 VI
圖目錄 VII
第一章 緒論 1
1.1 前言 1
1.2 無元素法之發展 1
1.3 本文架構 4
第二章 控制方程式推導 5
2.1 古典板控制方程式 5
2.2 範例解析解 8
2.2.1 外圈簡支圓形板受均佈載重 8
2.2.2 外圈固定圓形板受線性載重 9
2.2.3 外圈簡支環形板受均佈載重 9
2.2.4 四邊簡支方形板受雙正弦載重 10
2.2.5 四邊簡支方形板受均佈載重 11
2.2.6 四邊簡支方形板受線性載重 12
2.2.7 兩邊簡支兩邊固定方形板受正弦載重 12
第三章 理論推導 14
3.1受束制之移動最小二乘法 15
3.2 Hermite type應用於古典板 17
3.3鄰近點與權重函數之選取 20
第四章 數值範例 21
4.1 外圈簡支圓形板受均佈載重 22
4.2 外圈固定圓形板受線性載重 22
4.3 外圈簡支環形板受均佈載重 23
4.4 四邊簡支方形板受雙正弦載重 24
4.5 四邊簡支方形板受均佈載重 24
4.6 四邊簡支方形板受線性載重 25
4.7 兩邊簡支兩邊固定方形板受正弦載重 26
第五章 結論 27
參考文獻 28

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