本文以葛勒金弱積分式分析古典平板受力行為，其中之形狀函數及其各階導數以無網格之微分再生核近似法(differential reproducing kernel approximation method，DRKM)計算，位移邊界條件以懲罰法處理，數值計算範例為分析四種不同形式的平板問題，分別為：四邊滾支承受正弦載重、四邊滾支承受均勻載重作用、四邊固定端受均勻載重作用、兩邊滾支承與兩邊固定支承承受均勻載重作用，利用數值分析得到的最大位移、最大彎矩的數值解與其解析解進行比較分析。

In this paper, we use element-free Galerkin method to analysis the behavior of plates under load. Where the shape function and its derivative are obtain by the differential reproducing kernel approximation and the displacement boundary condition are impored by the penalty method. In the numerical example we analysis three types of plates under various loading：simply supported rectangular plated under sinusoidal load, simply supported and uniformly loaded rectangular plates, rectangular plates with all edges built in, rectangular plates with two opposite edges simply supported and the other two edges clamped, and compare the maximum displacement and maximum moment with the analytical solution.

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