修正狄勞尼三角網格分割法與機械元件分析應用

Abstract

本論文嘗試提出一種修正的狄勞尼三角網格分割法，針對機械元件的結構與應力集中的特性來作適應性之有限元素網格建立，並且利用一些簡單的範例來闡述這個修正的方法。 全文內容圍繞在有限元素法分析過程的前處理部份。從最基本的幾何模型原理開始談起。其次介紹電腦繪圖的基本觀念。然後分別說明典型的狄勞尼三角化網格分割法與所提出的修正方法。再透過二維範例的有限元素計算結果與應力集中理論做比較，來驗證這個修正的網格分割方式。最後，根據這個方法實際去分割一個三維的機械元件模型並且做出結論。

The purpose of this thesis is to develop a modified Delaunay triangulation to generate adaptive finite-element-meshes for structures of machine parts for their stress concentration analysis. We illustrate the concept of the method with some simple examples. The content is centred on the pre-processing of finite-element-analysis procedure. It begins with the introduction of fundamental theories of geometric modeling and basic concepts of computer graphics. Then, elaborates the typical Delaunay triangulation and the mentioned modified method respectively. By comparing calculation results of two-dimension cases with stress concentration theory, we verify this modified method. Finally, we generate a three-dimension mesh physically based on this extended method, and make a conclusion.