本文採用滿足控制方程式之齊次解為基底函數建立移動最小二乘法以求解平板問題，本文方法重要優點為離散點函數值及其一階導數，以及邊界條件之殘值以加權最小二乘法建立以節點值、節點一階導數值和其邊界條件值所表達的近似函數，最後由近似函數與節點值與一階導數在節點上之一致性條件，即可解得節點上之變數值而得邊界值問題之近似解。
數值算例中,以不同邊界和載重的板,長寬比1與2之板作為計算範例，利用數值分析得到的位移、轉角、彎矩及剪力與其解析解進行比較及討論本方法的可行性和精度。

In this paper, we use the homogeneous solutions of the governing equation as the basis functions to estabilish a moving least square method to solve the plate problems. The novelty of this approach is that, using the moving least square technique, we attempt to reduce the weighted sum of the residuals that results from the approximation to the field variable and it's derivatives ,and the boundary conditions. The process lead to an interpolation function which is express in terms of the nodal value of the field variable, the nodal value of it's derivatives, and the nodal value of the homogeneous terms in the differential equation. According to the requirement of consistency of the interpolation function with its value at nodes, the point collocation technique was employed to determine the unknown nodal values, and so complete the process of determining an approximation solution to the given problem.
Various examples include the plates 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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