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.

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