本文採用齊次基底移動最小二乘法(Moving Least Square Method with Homogeneous Base)來分析二維彈力問題，本方法採用滿足微分方程之函數為基底函數，透過局部區域內離散點函數值資料與邊界條件以加權最小二乘法建立近似函數，最後由節點值與近似函數之一致性條件，即可求出在節點上之近似值，進而求得邊界值問題之近似解，在具有應力奇異性之區域則採用特徵函數為基底進行分析並計算應力強度因子。
數值算例中分析懸臂梁受剪力作用、懸臂梁受均勻拉力作用以及不同裂縫情形，並探討在奇異點附近之應力集中現象，由算例分析結果得知在奇異點附近採用奇異性基底函數，僅少數節點即可完整準確分析奇異性現象。

In this paper, we use Moving Least Square Method with Homogeneous Base to analysis two-dimensional elastic problems. This method uses the base function which satisfied the differential equations, we attempt to reduce the weighted sum of the residuals that results from the approximation to the field variable and the boundary conditions. The process lead to an interpolation which is express in terms of the nodal value of the field variable. 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 approximate solution to given problem. For the regions that have stress singularity, we use the singular eigen factions as the base functions and thus the stress intensity factors can be obtained directly from the solution.
In numerical examples, we use the present method to analysis the problems of a cantilever beam subject to shear load, a cantilever beam subject to axis load and various type of crack problems. The results show that the stress singularity phenomenal can be accurate molding with a coarse distribution of node.

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