本文主要利用無元素法(meshfree methods)，配合微分再生核近似法
(differential reproducing kernel approximation method,DRKAM)與微分再生核內插法(differential reproducing kernel interpolation method ,DRKIM)。由建立各節點之再生核形狀函數(reproducing kernel shape functions)及其各階導數，代入葛勒金弱式(Galerkin weak formulation)求解二維彈力問題，藉此驗證此法之適用性及可行性。由於節點分佈方式不同，使得高斯積分點求解出的形狀函數也不盡相同，本文在求解含孔之無限板算例中，將節點分佈方式分為二次曲線佈點與均勻佈點，最後再探討其分佈方式不同所造成的精度上差異。
數值算例中求解承受單向軸力與剪力問題時，將同時以微分再生核中的近似法與內插法做分析，由數值結果可知使用內插法分析較近似法分析所得之結果來得穩定。

In this paper, based on meshfree methods coupled with differential reproducing kernel approximation method, (DRKAM) and differential reproducing kernel interpolation Method, (DRKIM). We established the reproducing kernel shape functions and its derivatives of each nodes and using Galerkin weak formulation solve the 2D elasticity problems.
Different distribution of nodes made different shape functions and affect the calculation precision. In solving the problem of a plate with circular hole, we use two different type of distribution of nodes to explores the effect of distribution of nodes on the precision of result.
In numerical examples, we study the problems of a cantilever beam subject to axis load and end shear load, analyses are made with DRKAM and DRKIM, compare the result of them. The results show that the DRKIM are more stable then DRKAM.

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