本文採用了受束制之移動最小二乘法(Constrained Moving Least Square Method)來分析二維彈性力學之相關問題。此一數值方法之特色為，在利用移動最小二乘法建立局部近似函數的同時加入限制，令其滿足控制方程式與邊界條件，使模擬出之函數值或其各階導數，均可滿足對應的微分方程式與邊界條件。
文中模擬了懸臂樑受剪力與受拉力作用，開孔無限板受拉力作用等問題，透過不同的基底階數、佈點數與佈點方式等因素，討論此數值方法之適用性，並與解析解相比較，分析其收斂率與誤差，以驗證本文所使用數值方法之正確性。

In this thesis, we use the constrained moving least square method is used to solve the planar elasticity problems. The novelty of this approach is that, we appropriate constraints into the moving least square method , so that it satisfy the governing equations and boundary conditions. So that the approximate function satisfy the governing equations and boundary conditions.
Using the present method, we simulate the cantilever beam loaded by shear and tensile force and the infinite plate with a hole loaded by the tensile force. In the example, we use different order of the base functions, different number of points and different point distributions to discuss the applicability of this method, and compare the numerical result with the exact solution to examine the accuracy and the rate of convergence of this method.

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