### 博碩士論文 90322036 詳細資訊

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(Numerical Simulations for a 3D System Composed of Polyhedral Blocks)

 ★ 多面塊體系統之運動模擬 ★ 元素釋放法在非均質材料之應用 ★ 元素釋放法在材料界面之處理 ★ 三維離散元素法數值模擬之改良 ★ 元素釋放法在滲流上的應用 ★ 三維顆粒介質與變形體互制行為之數值模擬 ★ 台北天母地下鋼構停車場規劃設計考量與施工問題之探討 ★ 元素釋放法於三維滲流之應用 ★ 無元素法加權函數的適用性 ★ 元素釋放法於單向度壓密理論之應用 ★ 混合型剛體顆粒系統之數值模擬 ★ 多面塊體數值模擬-塊體的切割 ★ 卵形顆粒介質運動之數值模擬 ★ 蛋形顆粒與多面體塊體之數值模擬

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The main difference between a polyhedral block and other discrete particles is the possible irregular shape of a polyhedral block. Different shapes of blocks can be generated for various kinds of problems. In this research, immovable blocks are used to simulate rock slopes and concrete walls. The contact behavior among the block, the slope, and the wall is studied when the block moves along the slope and finally stops by the wall. Besides, assembly of blocks is used to study fundamental problems in soil mechanics such as the lateral earth pressure and the angle at rest.

★ 旋轉矩陣
★ 接觸判斷

★ contact detection
★ rotation matrix

1.1 前言....................................................................................... 1
1.2 研究動機與目的.................................................................... 2
1.3 研究工具.............................................................................. 3
1.4 論文內容............................................................................... 3

2.1 分離元素法之發展過程......................................................... 5
2.1.1 二維圓形與橢圓顆粒系統.................................................. 5
2.1.2 二維塊體系統..................................................................... 6
2.1.3 三維圓球與橢球顆粒系統.................................................. 6
2.1.4 三維塊體系統..................................................................... 7

3.1 多面體體積與慣性張量之計算.............................................. 8
3.2 多面體系統之接觸判斷準則................................................. 9
3.2.1 接觸偵測..................................................................... 9
3.2.2 接觸型態之判斷.........................................................10
3.3 頂點對面之接觸判斷法則....................................................10
3.3.1 頂點入侵塊體之判斷法.............................................12
3.3.2 頂點入侵面之判斷法.................................................12
3.4 稜邊對稜邊之接觸判斷法則................................................14
3.5 接觸塊體之入侵量計算........................................................16
3.5.1 頂點對面接觸之入侵量計算......................................16
3.5.2 稜邊對稜邊接觸之入侵量計算..................................18
3.6 接觸力分析...........................................................................18
3.6.1 接觸力計算................................................................19
3.6.2 塊體物理量之描述與接觸機制..................................20
3.7 各時間步程內之運動分析....................................................22
3.7.1 塊體之運動方程式.....................................................22
3.7.2 塊體的新位置............................................................24
3.7.3 面與稜邊法向量之更新.............................................26

4.1 多面塊體數值程式之運算流程.............................................39
4.2 多面塊體程式對旋轉運動之驗證........................................40
4.3 多面塊體程式塊體接觸之驗證............................................41
4.3.1 多面塊體程式塊體稜邊對面接觸之驗證..................41
4.3.2 多面塊體程式塊體面對面接觸之驗證......................43
4.4 多面塊體程式塊體與邊界接觸之驗證.................................45

5.1 多面塊體堆積體..................................................................63
5.2 邊坡落石模擬試驗..............................................................65
5.3 側向土壓力分析...................................................................66
5.4 安息角模擬試驗..................................................................66

6.1 結論.....................................................................................77
6.2 建議.....................................................................................79

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