本文採用了基於狀態變數(State Variable)與Hermite型置點法(Hermite Type Collocation)之移動最小二乘法(Moving Least Square Method)來模擬二維彈性力學問題。狀態變數法是將原本為高階導數控制方程式以狀態空間(State Space)之概念，將其降階為多個低階導數方程式，再由移動最小二乘法理論求解變數；Hermite型置點法則只對主要變數進行近似，而在置點時將導數項變數同時納入置點，在此兩種變數設定下求解導數近似函數不需再做數值微分計算，即也可一次求解出所有變數。
本文模擬分析了懸臂梁受剪力、拉力作用，及無限板中央水平裂縫、中央開圓孔受拉力作用等二維彈性力學問題，經由改變基底階數、佈點型式、佈點密度等變因，與解析解或其問題本質之物理現象做比較，以討論數值方法模擬成果及適用性。

In this thesis, we use the moving least square methods which based on state variables and Hermite type collocation to analysis the two dimensional elasticity problem. In the state variable approach, we use the concept of state space which reduces the original higher-order differential equations to the systems of first-order differential equations, then solving these equations by the moving least square method. In the Hermite type collocation method, only the essential variables are approximated, and there derivatives are considered in the collocation. With these two kind of variables setting, we can solve all of the variables without any numerical differentiation.

Using the present method, this paper simulates the cantilever beams loaded by shear force or tensile force, and the infinite plates which have a central horizontal crack or a central hole loaded by the tensile force. In the example, we change different order of the base function, different types of the distribution and the different density of the distribution to compare with the exact solution or physical phenomena, and then discuss the results of numerical simulation and applicability.

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