本文應用齊次基底移動最小二乘法(Moving Least Square Method with Homogeneous Base)來分析二維扭轉問題。本方法在局部區域以滿足微分方程式之函數為基底函數，由離散點上之函數近似以及邊界條件，採用移動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。本文最後以橢圓形、正三角形和矩形等斷面之均質桿件受扭問題與矩形和圓形等斷面之複合桿件受扭問題作為計算範例，並且與解析解進行比較和分析數值收斂結果來驗證及討論本文方法之正確性與可行性。

In this paper, we present a Moving Least Square Method with Homogeneous Base for solving the torsional problems. The novelty of this method is that, in the local area using the basis function which satisfied the governing equation, 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 leads to an interpolation expressed 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 thus the approximate solution can be obtained. The accuracy and the rate of convergency of this method can be demonstrated by various examples including the problems of torsion of elastic shaft or composite bars.

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