臺灣博碩士論文加值系統

有限元素法發展至今已漸趨成熟與完整，然而有限元素法仍有一些不易解決的問題，例如：遇到較大變形、兩個不一樣材料的邊界以及裂縫時，在元素邊界的地方，會遇到應力或變位無法連續。
近年來，有一群學者試著尋找其他方法，想解決有限元素法所無法解決的問題，也能得到更精確的答案；他們打破元素的觀念，在一個範圍內建立節點，每個節點即可視為一個元素，每個節點有它各自的影響範圍，影響範圍的大小、形狀，與選擇的權重函數有關，各個節點的影響範圍可以重疊，利用移動式最小平方和方法找出其形狀函數，再推導勁度矩陣，即可建立模擬函數。
由於無元素方法發展至今不過十多年左右，本論文注重於公式的推導及對於本方法的一個發展做一個深入的整理，其次整理推導出一維的通式，寫成FORTRAN程式，對一些簡單的軸力桿件問題求解，顯現此一方法跟傳統有限元素法的差異。

The finite element method has been mature and complete up to now.But this method still has some problems not easy to solve. The large deformation problem, composite material problem and crack problem are example of it. Stress and displacements are not continuous over the element boundary.
In recent years, a group of scholars tried to find other methods to solve the problems that finite element method can''''t solve, and also tried to get more exact solution. They broke the concept of the element and set points in a domain. Every point can be taken as an element and every point has its own influence range and shape. Choosing weighting function is important for this method. The influence range of every point can overlap each other. The MLSA was used to find the shape function and stiffness matrix. Finally the simulation function can be established.
Since the element free method was developed about ten years, this paper emphasizes on getting the general formula in one dimension. A FORTRAN program for one dimensional problem was developed. This program can solve axial problems. The difference between the element free method and finite element method was discussed also.

第一章緒論
1.1 研究動機
1.2 研究目的
1.3 研究內容
1.4 文獻回顧
第二章 無網格法
2.1無網格法的發展
2.2移動式最小平方和方法
2.3 權重函數的選擇
第三章 一維的無元素法
3.1 前言
3.2 一維軸力桿件的勁度矩陣
第四章 實例
4.1 各種權重函數及形狀函數的圖形
4.2 不同點數對答案的影響
4.3 兩邊固定端的例題
4.4一端固定端一端自由端的例題
4.5 不均勻點的例題例題
4.6 簡單的裂縫例題
4.7 不均勻桿件例題
第五章 結論與建議
5.1 結論
5-2 建議與未來發展

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