B-Spline有限元素法是使用B-Spline函數來取代傳統有限元素法的基底函數的方法，此方法具有Ck-2連續性的狀態變數，其中k為B-Spline函數最高階數加一。為了讓基底函數在每一細胞元素交接處能有Ck-2連續性，所以必須讓每一塊細胞元素尺寸一樣。細胞元素為用於積分的方形子區域。
本論文中所使用的計算幾何理論為二元空間分割法(binary space partition)，此方法會對本身多邊形進行分割，我們可以利用這個特性去進行幾何圖形的布林運算。因此對於欲分析的幾何圖形所作的細胞元素網格化的動作亦是利用幾何圖形和各細胞元素進行一連串的布林運算交集測試所得的結果，在對於不規則幾何圖形的部份，程式會對和此圖形不規則邊界相交的細胞元素，進行邊界的處理，和包含於細胞元素中的幾何實體進行切割的動作。
在二維平板的實例測試中，分別針對規則與不規則形狀的平板作分析，我們發現B-Spline有限元素法可以利用較少自由度計算出和有限元素法相近的位移與應力結果。

B-Spline finite element method is a numerical method which using B-Spline basis functions instead of finite element method basis function. The state variables of the B-Spline functions have Ck-2 continuity, where k is the order of the polynomials in B-Spline functions plus one. In order to enable the basis functions have Ck-2 continuity at boundaries between every cell, we should make the size of each cell the same. The cell is the square subdomain used for integration.
The computational geometry theory used in this study is the Binary space partition. This method will spilt the polygon and we can use this property to proceed Boolean operation of geometric polygon. The cell mesh of the geometric polygon in the analysis is the results of a series of intersection test to the irregular geometric polygon. The program will deal with the boundaries between the polygon and intersected cell, and spilt the geometric solids included in the cell.
We analyze the regular and the irregular shape plates in the two dimensional problems. In these plate examples, we find that the accuracy of the displacements and the stresses of B-Spline finite element method are almost the same as in the finite element method, but the degree of freedom in B-Spline finite element method is much less than finite element method.

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