臺灣博碩士論文加值系統

中文摘要
本研究發展元素釋放法(Element Free Method, EFM)計算機程式來模擬地下水滲流的問題，並比較元素釋放法與Lagrange有限元素法程式SEEP在準確性與計算時間上之優劣。
Lagrange有限元素法在處理非侷限流時，需針對邊界條件作元素網格重建之處置，且初始狀況的網格與節點建立需花費較多時間。元素釋放法是基於移動式最小平方(Moving Least Squares, MLS)內差的觀念來處理定義域內節點資料之一種無網格(Meshless)的數值分析方法，只需離散節點的資料即可建立形狀函數，沒有節點與元素間關係之限制，因此可省下輸入資料的時間。
對於非滲透性結構物造成節點影響範圍的改變，本文採用通視原則修正節點搜尋的範圍，並採用權值調整法來處理積分網格非完全包含於定義域內之問題。對土壩滲流問題以不重新組立網格而改由增加節點的方式，依滲流線的邊界條件進行疊代計算。

ABSTRACT
A computer code based on the element free method to simulate the seepage behavior is developed in this research. Comparisons, specifically on accuracy and efficiency, are made between the newly developed code and the Lagrange finite element program SEEP.
In analyzing unconfined flow problems, remesh is general used in finite element code as is in the SEEP. Besides, construction of the initial element mesh for the input data file is more or less time consuming. Element free method is a meshless numerical technique based on the concept of Moving Least Squares, which interpolates the data of various nodal points within the domain to be analyzed. Shape functions, similar to those in the finite element method, are formed based on a base function and a weight function along with related nodal data for each reference point. Connectivity between nodes and elements is thus freed and saves efforts for the related input.
The influence circle is sometimes obstructed by the boundary due to various geometry of analyzing domain and a rule of determining the nodal influence circle is developed. Gauss integration is used and its result is adjusted while the domain is not perfectly matched by the integration cell. An improved result is obtained by adding nodes on the line of seepage during iteration in simulating the seepage behavior of an earth dam.

中文摘要I
英文摘要II
目錄 III
圖目錄 VI
表目錄IX
第一章 緒論1
1-1 前言 1
1-2 研究動機與目的2
1-3 論文內容3
第二章 文獻回顧5
2-1 移動式最小平方法(M LS)5
2-2 元素釋放法5
2-2.1 擴散元素法(Diffuse Element Method, DEM)5
2-2.2 元素釋放法(Element Free Galerkin Method, EFGM)6
2-3高斯積分之權值調整法6
2-3.1高斯積分法新義6
2-3.2不規則邊界處之積分處理7
2-4多孔隙滲流理論8
第三章 元素釋放法用於滲流方程式之推導12
3-1 控制方程式12
3-2 變分方程式15
3-3 形狀函數之推導17
3-4 邊界處理22
3-5 流量處理25
第四章 元素釋放法在滲流之應用26
4-1通視原則對節點影響範圍之修正26
4-2節點與積分網格之配置29
4-3高斯積分權重之計算32
4-4節點增設原則39
4-5節點在定義域外之處理方式43
4-6高斯積分點於通視判斷下之處理方式44
4-7程式分析流程46
第五章 數值算例53
5-1誤差評估53
5-2單向度滲流54
5-2.1 單向度滲流案例54
5-2.2 節點與網格配置原則55
5-3侷限流（版樁滲流）58
5-4 非侷限流59
5-4.1.1 SEEP程式之輸入資料59
5-4.1.2 SEEP計算結果59
5-4.1.3 梯形-元素釋放法之輸入資料61
5-4.1.4元素釋放法之計算結果61
5-4.1.5邊界節點之增設65
5-4.1.6邊界節點增設之計算結果65
5-4.1.7元素釋放法與SEEP程式之計算結果比較69
第六章 結論與建議70
6-1結論70
6-2建議71

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