本研究提出一虛擬質點之概念，藉由有限元素法位移內插得到虛擬質點位移參數之特性，將有限元素法與元素釋放法聯結使用。內容包含三個部份：一、以虛擬質點將有限元素法位移場與元素釋放法位移場結合；二、將有限元素法不連續梯度場藉由虛擬質點與移動式最小誤差平方和修復成連續梯度場；三、以不收斂之有限元素法結果為基礎，將元素釋放法依虛擬質點順序，進行局部力平衡疊代求解。
　　本研究成果顯示，藉由虛擬質點的增加，可將有限元素法區域與元素釋放法區域更有效接合，並減少兩區域邊界位移與梯度差異量。亦可因虛擬質點數量增加，使修復後之平滑化位移場與梯度場更接近有限元素法結果。局部力平衡疊代求解，也因虛擬質點數量增加，而改善數值模擬結果。

A concept of “virtual particles” is developed in this study. Virtual particles are interpolated from the finite element displacement field. Through the usage of virtual particles, both element free Galerkin method and finite element method can be combined in an analysis. Three problems are solved in this study. The first is to combine both displacement fields; the second is to present the solved finite element displacement field by element free formulation; The third is an iterative solution procedure by the element free formulation.
The obtained results show that virtual particles can combine two displacement fields success fully. Also, both the displacement field and the strain field are continuous. The iterative solution procedure can improve the local solution accuracy.

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