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研究生： 謝宜典
I-Tien Shueh
論文名稱： 無元素葛勒金法
Element Free Galerkin Method
指導教授： 鄔蜀威
Shu-Wei Wu
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 機械工程學系
Department of Mechanical Engineering
畢業學年度： 94
語文別： 中文
論文頁數： 46
中文關鍵詞： 無網格法 、無元素法 、變動最小二乘法 、無元素葛勒金法
外文關鍵詞： MLS, Meshfree, Meshless, EFG
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    • 本文將介紹無元素葛勒金法，此無元素法為利用變動最小二乘法所求的近似函數引入葛勒金弱式推導。可克服有限元素在工程上的限制。例如：鎖死、大變形問題精確度降低及裂縫成長等問題。本文將以靜彈性力學為例，說明標準補丁測試、懸臂梁和中間挖孔平板，並討論精確度與收斂性。也提供了Fortran程式碼，可供發展應用軟體或為撰寫其他無元素法程式參考。
    本文包括無元素葛勒金法、變動最小二乘法基本原理及三個數值範例與無元素葛勒金法懲罰法Fortran程式碼。

    An element-free Galerkin(EFG) method is introduced in this paper. It is an meshfree method. In this method, moving least-square interpolates are used to construct the approximate function for the Galerkin weak-form. EFG can overcome finite element method(FEM) several limitations in the engineering. For example, locking, large deformation problems accuracy losing, and crack growth problems. In this study, EFG is applied to elastostatics analysis. Path test, cantilevered beam, and plate with a central circular hole will be computed in this paper. Accuracy and convergence are also discussed in this paper. In addition, EFG method Fortran code also is offered in this paper. This Fortran code can be developed to meshfree application software or other meshfree method in the further.

    目 錄 中文摘要................................................................... I 英文摘要….............................................................. II 圖目錄...................................................................... III 表目錄...................................................................... IV 目錄…...................................................................... V 第一章 序論 1.1 前言................................................................... 1 1.2 文獻回顧........................................................... 1 1.3 研究目的........................................................... 4 1.3 本文架構........................................................... 5 第二章 移動最小平方法 2.1 前言................................................................... 6 2.2 基本理論........................................................... 6 2.2 權重函數........................................................... 10 第三章 無網格葛勒金懲罰法 3.1 前言................................................................... 12 3.2 靜彈性力學公式............................................... 13 3.3 葛勒金弱式懲罰法........................................... 13 3.4 程式執行流程................................................... 18 第四章 數值範例 4.1 前言…............................................................... 19 4.2 範例1：標準補丁測試.................................... 19 4.3 範例2：懸臂梁................................................ 22 4.4 範例3：中間挖有圓孔平板............................ 26 第五章 結論與未來發展 5.1 結論................................................................... 31 5.2 未來發展........................................................... 31 參考文獻.......................................................................... 32 附錄.................................................................................. 34

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