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研究生： 李世昌
Shih-chang Lee
論文名稱： 三維多面塊體系統之數值模擬
Numerical Simulations for a 3D System Composed of Polyhedral Blocks
指導教授： 盛若磐
Jopan Sheng
口試委員:
學位類別： 碩士
Master
系所名稱： 工學院 - 土木工程學系
Department of Civil Engineering
畢業學年度： 91
語文別： 中文
論文頁數： 103
中文關鍵詞： 塊體形狀 、旋轉矩陣 、接觸判斷
外文關鍵詞： shape of polyhedral block, contact detection, rotation matrix
相關次數： 點閱：11  下載：0 
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    • 三維空間中之多面塊體由頂點、稜邊及面所組成，經由此三者的相互接觸構成了塊體間的碰撞行為。本研究基於許秀真之多面塊體系統模擬程式，利用頂點對面以及稜邊對稜邊之接觸判斷，完成各種複雜的接觸行為，並以牛頓第二運動定理與尤拉運動方程式，處理每個步程中塊體接觸受力後之運動行為。在處理塊體旋轉運動時，使用了旋轉矩陣對塊體質心至各頂點向量進行計算，使向量方向指向頂點之新位置，向量大小維持不變，如此可使塊體體積不因旋轉運動而改變。
    多面塊體與其他離散體的最大不同處在於多面塊體外形的不規則，利用此一特點，可以針對不同的問題設計不同的塊體形狀。研究中嘗試控制塊體的運動使其成為不動塊體，以此類塊體模擬固定之構造物如斜坡與攔石柵，進行邊坡落石的模擬試驗，觀察不同參數下落石與構造物間之碰撞行為。研究中更嘗試建立多數塊體之堆積體，並以堆積體進行大地工程中之側向土壓力與安息角之試驗模擬。

    A polyhedral block is composed of planes, edges, and vertices in a 3D space. The contact between two blocks could be any contact among these three parts. This research is based on a computer code of a polyhedral block system written by Hsiu-chen Hsu. Contact types are categorized by contacts of vertex-to-face and edge-to-edge only. After all the contact forces on each block are estimated, Newton’s Second Law and Euler’s Equations of motion are used in computing the motion of each block for a chosen small time interval. A rotation matrix is used here to compute the motion of each vertex when a block rotates. This method changes the direction of the position vector of each vertex of a rotating block but keeps its magnitude constant. This quarantees a constant volume for a rigid block as it is assumed in this research.
    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.

    摘要...................................................................................................1 英文摘要......................................................................................... II 目錄.................................................................................................III 圖目錄..............................................................................................V 表目錄..........................................................................................VIII 符號說明........................................................................................IX 第一章緒論....................................................................................1 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 第二章文獻回顧...........................................................................5 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 第三章多面體力學模擬程式之理論推導.................................8 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 第四章塊體模擬程式之驗證....................................................39 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 第五章多面塊體堆積體建立與程式應用...............................63 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 第六章結論與建議.....................................................................77 6.1 結論.....................................................................................77 6.2 建議.....................................................................................79 參考文獻........................................................................................81 附錄一：Simplex 積分法...........................................................84 附錄二：全域與局部座標系之轉換.........................................90

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