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研究生:陳慶賢
研究生(外文):Chin-Hsen Chen
論文名稱:顆粒介質數值模擬之人工透射邊界
論文名稱(外文):A Transmitting Boundary Model for the Numerical Simulation of Granular Media
指導教授:王仲宇
指導教授(外文):Chung-Yue Wang
學位類別:碩士
校院名稱:國立中央大學
系所名稱:土木工程研究所
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:1999
畢業學年度:87
語文別:中文
論文頁數:83
中文關鍵詞:透射邊界顆粒的波傳顯式有限元
外文關鍵詞:transmitting boundarygranularwave propagationexplicit finite element
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本論文採用多次透射公式配合顯性有限元素法應用於三維離散顆粒模
擬,發展一種新的數值分析模擬方法。多次透射公式能消除數值模型邊界
產生的反射波,所以這個新方法能夠在近場區實現無限域顆粒介質的動態
接觸問題。本論文探討多次透射公式的收斂特性以及穩定性,並發展程式
驗證其正確性﹔此外,還探討平滑方法對於多次透射公式穩定實施的改善
以及對模擬準確性的影響。最後於顆粒模擬的固定邊界之外,建立有限元
素透射層,來達到消除反射波模擬顆粒群體關係的目的。

In this thesis, adopting the multi-transmitting boundary
schemes together with an explicit finite element model into a
3D discrete ball element code develops a new numerical
simulation method. The multi-transmitting scheme (MTS) can
eliminate the reflection from the computational boundary. This
new method can be applied to the analysis of dynamic contact
problems in infinite granular medium systems by a finite number
of particles in a near zone. The convergence and accuracy
criteria as well as a smooth technique for the stability for the
multi-transmitting boundary scheme are derived and studied in
detail. Several benchmark problems are studied to evaluate the
accuracy and capabilities of this newly proposed method in the
dynamic analysis of 3D granular medium.

摘要......................... Ⅰ
英文摘要....................... Ⅱ
目錄......................... Ⅲ
圖目錄........................ Ⅴ
第一章 序論.....................1
1-1 前言.................. 1
1-2 研究動機與目的............. 2
1-3 論文內容................ 4
第二章 文獻回顧................... 6
2-1 人工透射邊界條件.............. 6
2-2 離散元素法................. 8
第三章 人工透射邊界之基礎理論介紹..........11
3-1 人工透射邊界條件............ 11
3-2 多次透射公式.............. 13
3-3 反射係數................ 18
3-4 多次透射公式的實用形式......... 23
3-5 穩定實現多次透射公式的措施....... 25
3-6 多項透射邊界條件............ 26
第四章 顯式時間積分法................ 32
4-1 Central difference method........... 32
4-2 N階多次透射公式與顯式積分之結合..... 34
第五章 人工透射邊界條件與顆粒介質模擬之結合..... 36
5-1 顆粒模擬的透射邊界............ 36
5-2 如何在顆粒模擬中實施透射邊界....... 37
5-3 顆粒模擬中放置透射邊界之步驟....... 37
第六章 程式驗證與討論................ 39
第七章 結論與建議.................. 42
參考文獻....................... 46
附錄一........................ 78
附錄二........................ 83

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