摘要

　　本研究主要在分析與比較目前各種將二維圖形狄勞尼三角網格化及三維圖形狄勞尼四面體化的各種演算法，並探討各種網格化演算法使用於有限元素分析軟體中的效果。
　　本文有效地經由所撰寫的Matlab程式碼，將二維三角網格產生器Triangle、三維四面體網格產生器TetGen分別與本研究室自行開發的有限元素法程式結合。透過二維平面應力與三維實體之範例的分析與模擬，最後與商用軟體ANSYS相驗證。由本文的模擬結果與ANSYS的輸出數據相比較後，可發現二者十分相近。

Abstract
　　The main goal of this research was to compare the algorithms to triangularlize the two dimensional geometry and to tetrahedrilize the three dimensional geometry. The effect of the above algorithms to be used in the finite element calculations was studied.
　　The two dimensional triangulation mesh generation code Triangle and the three dimensional tetrahedrization mesh generation code TetGen was combined with our finite element code by the use of the Matlab programming language. Two dimensional plane stress and three dimensional solid problems were used as examples to show the effect of our code. When compared with the results from the commercial code ANSYS, the results from our code are similar to the results from ANSYS.

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