博碩士論文 101322004 詳細資訊




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姓名 林鴻(Hung-Lin)  查詢紙本館藏   畢業系所 土木工程學系
論文名稱 以四面體離散化多面體系統之接觸分析與模擬
(Contact Analysis and Numerical Simmulation of Polyhedral Blocks Discretizedc by Tetrahedrons)
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摘要(中) 本論文針對多面體顆粒間的接觸,基於許秀真的接觸判斷理論(頂點對面接觸判斷、稜邊對稜邊接觸判斷),進行了四面體之接觸研究。本研究有將四面體的各種接觸情形做分類,有頂點對頂點、頂點對稜邊、頂點對頂點、稜邊對稜邊、稜邊對面、面對面六大類。以往的多面體接觸其接觸判斷單位皆為任意的多面體接觸,接觸情況較為複雜,本研究意圖減少接觸情況的複雜程度,將任意的多面體之接觸轉變為四面體群間的接觸判斷(一個多面體為一個四面體群)。相信多面體間的接觸判斷改為四面體群間的接觸判斷是必然的,因為變形和分離的問題是要將多面體切割成多個元素,才能分析其內部的行為。
兩相同的多面體碰撞組合,有切割成多個元素後的碰撞與未經切割成多個元素的碰撞,發現有經切割成多個元素的接觸判斷方法若沿用許秀真的接觸判斷方法會有重複計算的錯誤,本論文有提出新的接處點篩選方法進行處理,即可等同於原來未經切割成多個元素的多面體碰撞行為。
對於接觸偵測本研究有提出全新的想法視窗面法,構想是尋找兩接觸塊體之間可以代表入侵或分開的一最佳視角,作為可以接觸偵測的方法。另外,本研究也改良傳統之包絡面法變為新的包絡面法以改善接觸誤判的情形。
摘要(英) The paper aims to contact of polyhedral particles, On the basis of the theory of contact detection offered by Hsiu-chen Hsu (Vertex-to-Face contact detection and Edge-to-Edge contact detection), carrying on the investigation of Tetrahedron-to-Tetrahedron contact. This study classify Tetrahedron-to-Tetrahedron contact situations,there are six assembles of Tetrahedron-to-Tetrahedron contact situations :Vertex-to-Vertex、Vertex-to-Edge、Vertex-to-Face、Edge-to-Edge、Edge-to-Face、Face-to-Face. Traditional contact of polyhedral particles, contact judgement unit is one random shape particle means the polyhedron- to -polyhedron contact is more difficult and complex than the Tetrahedron-to-Tetrahedron contact. This sturdy intends to reduce the complex level of contact, random shaping polyhedron-to -polyhedron contact transform uniform shaping Tetrahedron- to-Tetrahedron contact (one polyhedron has two or more Tetrahedrons), polyhedron- to -polyhedron contact Transforms to Tetrahedron-to-Tetrahedron contact must be the tendency, because deforming and discrete problem needs to analysis the elements cutting from polyhedron, then could discuss internal Phenomenon of polyhedron-to -polyhedron contact.
The two same polyhedron-to -polyhedron contact assembles, the result with polyhedron cutting to some tetrahedrons and the result with polyhedron no cutting to some tetrahedrons are different, if using traditional contact judgement method(Hsiu-chen Hsu whose method),the result with polyhedron cutting to some tetrahedrons change to weird, appearing unreasonable translation and rotation. By the study, finding out if Tetrahedron-to-Tetrahedron contact using traditional contact judgement method has the problem with repeat counting contact nodal points causing motion error.
The study provides new thought Rotating-window-plane method about contact detection, the thought is trying to seeking the obviously separating view of two non-contact polyhedrons or less closing view between two non-contact polyhedrons.Rotating observing window with Ball-coordinate then projenting polyhedrons to observing window to judge wheter contact or non-contact.The Cutting-plane method has highly accuracy and easy understanding, which is more accurate than traditional envelope method.The study also improve traditional envelope method to new envelope method, to less missing catching contact.
關鍵字(中) ★ 多面體
★ 接觸偵測
★ 四面體化
★ 視窗面法
關鍵字(英) ★ polyhedron
★ contact detection
★ tetrahedron
★ rotating-window-plane
論文目次 摘要 I
ABSTRACT II
目錄 III
圖目錄 VI
表目錄 XII
第一章 緒論 1
1.1前言 1
1.2研究動機與目的 1
1.3論文內容 1
第二章 文獻回顧 2
2.1離散元素法發展簡史 2
第三章 理論推導 3
3.1視窗面法 3
3.1.1視窗面的想法 3
3.1.2觀測球的建立 4
3.1.3視窗面的影像建立 5
3.1.4視窗面上的正交曲線座標 7
3.1.5兩投影接觸判斷 11
3.1.6兩塊體的接觸偵測 13
3.2新包絡面法 14
3.3四面體系統之接觸判斷 17
3.3.1四面體系統之接觸型態 17
I.頂點對頂點接觸 17
II.頂點與稜邊接觸 18
III.稜邊對面接觸 18
IV.面對面接觸 19
3.4四面體化頂點對面的接觸判斷法則 22
3.4.1 四面體化頂點對面的接觸判斷法則所用到的概念 22
3.4.2 四面體化頂點對面之接觸判斷法則流程 27
3.5四面體化稜邊對稜邊之接觸判斷法則 28
3.5.1四面體化稜邊對稜邊的接觸判斷法則所用到的特點 28
3.5.2四面體化稜邊對稜邊之接觸判斷法則流程 33
3.6接觸塊體之入侵量計算 34
3.6.1頂點對面接觸之型態分類 34
3.6.2頂點對面接觸之入侵量計算 34
3.6.3稜邊對稜邊接觸之入侵量計算 36
3.7接觸塊體之接觸力計算 38
3.7.1正向接觸力計算 39
3.7.2切向接觸力計算 40
3.7.3接觸力計算流程 42
3.8多面體之運動方程式 43
3.8.1 塊體之平移加速度與旋轉加速度 43
3.8.2多面體之運動方程式以中央差分法表示 44
3.8.3多面體之平移與以大旋轉角旋轉 45
3.9.接觸分析系統流程與接觸點處理 48
3.9.1 新舊接觸判斷法差異與接觸點處理 52
第四章 數值算例 55
4.1接觸型態測試 55
4.1.1正心頂點對面碰撞 55
4.1.2偏心頂點對面碰撞 58
4.1.3正心頂點對稜邊碰撞 63
4.1.4偏心頂點對稜邊碰撞 66
4.1.5正心頂點對頂點碰撞 71
4.1.6正心稜邊對稜邊十字碰撞 74
4.1.7偏心稜邊對稜邊十字碰撞 77
4.1.8正心稜邊對稜邊一字碰撞 82
4.1.9偏心稜邊對稜邊一字碰撞 85
4.1.10正心稜邊對面碰撞 90
4.1.11偏心稜邊對面碰撞 93
4.1.12正心面對面碰撞 98
4.1.13偏心面對面碰撞 101
4.2摩擦力測試 108
4.2.2傾斜角大於摩擦角測試 108
4.2.1傾斜角小於摩擦角測試 114
第五章 結論與建議 119
5.1結論 119
5.2建議 120
參考文獻 121
附錄一:Simplex積分法 122
附錄二:全域與區域座標之轉換 126
附錄三:中央差分法 128
附錄四:剛體之平移與大旋轉 130

參考文獻 [1]Cundall, P. A., “Formulation of Three-dimensional Distinct Element Model—Part Ⅰ. A Scheme to Detect and Represent Contacts in a System Composed of Many Polyhedral Blocks,” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 25, No. 3, pp. 107-116 (1988).
[2] Cundall, P.A., “Formulation of a Three-dimensional Distinct Element Model— Part Ⅱ. Mechanical Calculations for Motion and Interaction of a System Composed of Many Polyhedral Blocks.” Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., Vol. 25, No. 3, pp. 117-125 (1988).
[3] Cundall, P.A., and O.D.L. Strack, “A Discrete Numerical Model for Granular Assemblies,” Geotechnique, Vol. 29, No. 1, pp. 47-65 (1979).
[4] Shi, G.H.,“Discontinuous Deformation Analysis, A new Numerical Model for the Static and Dynamics of Block systems,”Ph. D. Thesis, Department of Civil Engineering, University of California at Berkeley (1988).
[5] Jian-Hong Wu, “New Vertex-to-Face Contact Calculating Algorithm in Three-Dimensional Discrete Numerical Analysis”, Advances in Engineering Software , (2007).
[6] .Jian-Hong Wu, “New Edge-to-Edge Contact Calculating Algorithm in Three-Dimensional Discrete Numerical Analysis”, Advances in Engineering Software , (2007).
[7] S.-W. Chang and C. S. Chen (2008), "A Non-iterative Derivation of the Common Plane for Contact Detection of Polyhedral Blocks," International Journal for Numerical Methods in Engineering, Vol. 74, Issue 5, April, pp. 734-753
[8] 許秀真,「多面塊體系統之運動模擬」,碩士論文,國立中央大學土木工程系,中壢(2001)。
[9] 李世昌,「三維多面塊體系統之數值模擬」,碩士論文,國立中央大學土木工程系,中壢(2004)。
[10] 周靖江,「以數學規劃研究多面體離散元素在三維空間之接觸分析與運動模擬」,碩士論文,國立台灣大學土木工程研究所,台北,(2004)。
[11] 張君豪,「多面塊體數值模擬-塊體的切割」,碩士論文,國立中央大學土木工程系,中壢(2006)。
[12] 陳昭雄,「蛋形顆粒與多面體塊體之數值模擬」,碩士論文,國立中央大學土木工程系,中壢(2006)。
[13]石根華,「三維流形方法有限元滲流分析理論」,中興工程顧問社,台北(1999)。
指導教授 王仲宇(C.Y.Wang) 審核日期 2015-7-17
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