本文以具Ck-2連續性的B-spline函數為基底函數解三維不規則形狀彈性力學問題，並使用二至六階的B-spline函數針對不同網格大小下進行分析。B-spline有限元素法於一維與二維結構、熱傳、電磁場等工程問題逐漸有較多的文獻提到其應用，較少有文獻提及將其應用在處理三維不規則形狀問題，因此本文主要探討B-spline於三維不規則形狀問題的適用性。
首先針對立方實體中心內含空心圓球的例子，發現相對於傳統二階有限元素法，B-spline有限元素法能以較少的自由度得到接近收斂值的結果，表現出B-spline在自由度上的優勢。其後陸續測試立方實體內含空心橢圓柱及內含空心橢球的例子，發現當網格元素愈少，表現不出高階B-spline的收斂性，但當網格元素愈多，其高階收斂性的展現使得所求得的應力值接近於ANSYS的收斂值，且高階所花的自由度皆較ANSYS少很多，因此針對將B-spline有限元素法應用於三維不規則實體中，依舊如同一維與二維B-spline的優勢，能花相當少的自由度得到相當於ANSYS的收斂值。
最後提出三維細切方法，使得使用者可就關心的區域做局部更細密的網格化，以較少的自由度及元素個數求得更準確的結果。

We used the B-spline functions which has Ck-2 continuity as the basis functions to solve three dimensional elastic problems with irregular shapes. We use B-spline functions from second order to sixth order to analyze different element size on the problems with different irregular shapes. There are some papers using B-spline finite element method with structure, heat transfer and electromagnetic field problems in one and two dimensional problems now. There are less researchers using B-spline functions to analyze three dimensional elastic problems with irregular shapes. Therefore we study the applicability of B-spline finite element in three dimensional irregular problems.
The first irregular shape in these studies is a cube with a sphere hole. We find B-spline finite element method can use lesser degree of freedom to obtain the same accuracy compare with the traditional finite element method. A cube with a ellipse cylinder hole and a cube with a ellipsoid hole are used as the others irregular shapes examples in the thesis. In both cases, we find that it dosen’t show better result accuracy from high-order B-spline basis functions. When element numbers become larger, the effect of high order B-spline basis function is shown. In the situation, we obtain the stress result near the ANSYS’s stress convergence value. The high-order B-spline finite element method uses degree of freedom lesser than ANSYS. The application of B-spline finite element method in three dimensional irregular problems obtains the same stress convergence value results compare with the ANSYS with lesser degree of freedoms. Using B-spline in three dimensional irregular problems appears the advantage of degree of freedom as good as one and two dimensional problems.
Finally, we proposed a method of refinement for three dimensional. With this method, the user can focus concerning area with a finer mesh. We can use lesser degree of freedoms and elements to get a more accurate result with local fine mesh in the analysis.

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