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 .

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