本文提出以B-Spline函數作為有限元素法的基底函數， B-Spline函數可使狀態變數擁有Ck-2的連續性，其中k為B-Spline函數最高階數加一，如此便可以得到更準確的結果。
在一維問題中，將B-Spline函數階數由二階提高至三階，自由度只由原本的n+2提升至n+3，其中n是指元素的個數，而有限元素法則會使自由度由2n+1提升至3n+1。當二維物理問題使用三階多項式分析時，B-Spline有限元素法與有限元素法在自由度上的差異會變為(n+3)2與(3n+1)2，當階數往上增加時自由度上的差別會更大。使用B-Spline有限元素法便能在增加少量自由度的情況下增加階數。
在一維的實例測試中，使用B-Spline有限元素法，可在自由度小於有限元素法時，得到相同的應力精確度，而在自由度相同時，應力的誤差更是下降至有限元素法的十分之一 。而在二維的測試中，B-Spline有限元素法自由度與有限元素法自由度的差異會更加的明顯 。並在加入細切的功能之後，可使用較少的自由度得到更準確的值。如此便可以知道使用B-Spline函數作為基底函數可以大幅降低求解的時間，並可使應力值更為準確。

We use the B-Spline functions as the basis functions in the finite element method. Since the state variables in the B-Spline functions have Ck-2 continuity, where k is the order of the polynomials in the B-Spline functions plus one, we can gain more accurate results in the analysis.
For the B-Spline finite element method used in the one dimensional problem, when the order of the polynomials in the B-Spline functions is increased from second order to third order, the degree of freedom in the analysis will be increased from n+2 to n+3, where n is the number of the elements. However, the degree of freedom for the finite element analysis will be increased from 2n+1 to 3n+1. When the third order polynomials is used to solve the two dimensional problems, the difference in the degree of freedoms between B-Spline finite element method and finite element method will be (n+3)2 and (3n+1)2. As the order of the polynomials increased, the difference in the degree of freedom will be larger and larger. The degree of freedom in the B-Spline finite element analysis can be increased just a small amount when the order of the polynomials is increased.
In one dimensional test example, using B-Spline finite element method can gain the same accuracy of the stress when the degree of freedom is smaller than the degree of freedom in the finite element method. Moreover, when the degree of freedom is the same, the error of the stress decreases to one tenth of finite element method. In two dimensional test examples, the difference in the degree of freedoms between B-Spline finite element method and finite element method will be more obvious. After adding refinement capability, we can gain the better results by using less degree of freedoms. In summary, using B-Spline functions as basis functions can greatly decrease the computer solving time and make the stress value more accurate.

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