三維可變形多面體之接觸運動分析

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姓名	黃亮維(Liang-Wei Huang) 查詢紙本館藏	畢業系所	土木工程學系
論文名稱	三維可變形多面體之接觸運動分析 (3D Contact Analysis of Multiple Deformable Polyhedrons in Motion)
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摘要(中)	本論文提出一可模擬任意形狀之可變形多面體塊體運動之模擬程式，此程式建模是由數個四面體元素網格所構成的。而四面體元素之間的接觸，則是由稜邊對稜邊、頂點對面兩種基本幾何接觸型態來作分類並進行有效且快速的分析。本研究主要的分析流程是:在三維空間建立欲分析之幾何塊體形狀及依照需求之網格密度繪製好四面體元素網格，進行模擬之前須確認塊體材料性質，例如:各材料之楊氏係數、柏松比、材料密度、摩擦係數，以及該分析之外力歷時等。接下來先進來元素的分類，位於各塊體外表面的元素才有可能與其餘塊體之元素接觸，位於塊體內之元素就不可能有接觸；分類好欲詳細分析之元素後，透過本研究所撰寫之多層判斷式，在每個時刻預先作接觸可能之判斷，如果該接觸組合通過層層判斷式，接著就詳細計算該組合之正向、橫向入侵量，配合上接觸彈簧，得到作用於接觸點上之正向、橫向力向量，最後將其分配至構成接觸組合之質點上，完成一個時刻之接觸分析。本研究之分析方法優勢在於，塊體的質量集中於節點，並且由接觸點位置分配力向量，可使不同四面體單元對應不同之材料模數，於受力後反應出應有之變形。而因為有了層層之判斷式，故越複雜、冗長之計算皆是判斷有可能接觸後才使用，通過這樣的篩選可以加速模擬分析的進行。最後透過一些例題之模擬分析，驗證所發展之程序的合理性。
摘要(英)	This paper provides a new algorithm and a simulation code for 3D contact analysis of 3D deformable polyhedrons of any shape. Only the contact types of vertex-to-face and edge-to-edge are required for the eleven types of contact are theoretically possible between any two tetrahedron blocks. Traditional contact of polyhedron blocks are way more difficult than contact of tetrahedron blocks. This study intends to reduce the complex level of polyhedron blocks contact by using tetrahedron meshes. Cutting polyhedron blocks into tetrahedron meshes, then using contact detection methods among tetrahedron blocks. With the advantages of Vector Finite Elements Methods, this computer code can simulate contact behavior among multiple deformable polyhedrons in motion. To speed up this program, this study provides a function to the tetrahedron meshes. After we establishing the simulation model, we use mesh analysis to sort the tetrahedrons are the ones inside the polyhedron body or the ones with possible contact. Then we use the closed surface informations to analyze the contact problems. Some example problems are studied to verify the accuracy and capabilities of this newly proposed simulation code.
關鍵字(中)	★ 多面體 ★ 四面體元素 ★ 接觸搜尋 ★ 可變形體	關鍵字(英)	★ polyhedron ★ tetrahedron ★ contact detection ★ deformable body
論文目次	摘要 i 誌謝 iii 目錄 iv 圖目錄 vii 表目錄 x 第一章緒論 1 1.1 研究動機與目的 1 1.2 論文架構 2 1.3 研究工具 2 第二章文獻回顧 3 2.1 離散元素法之發展 3 2.2 二維塊體系統 3 2.3 三維離散系統之力學分析程序 4 2.4 共用平面概念 4 2.5 內外界搜尋法 5 2.6 一般自由面上多面節理生成與切割 5 2.7 流形切割及有限元網格覆蓋下的三維流形單元生成 6 2.8 流固耦合中接觸介面搜尋 6 2.9 有限元素法之接觸分析 7 2.10 凹面體接觸問題 7 2.11 多面塊體系統之運動模擬 7 2.12 以四面體離散化多面體系統之接觸分析與模擬 8 2.13 向量式有限元之研究與發展 8 第三章接觸理論 9 3.1 分析域內塊體建立與前處理 9 3.1.1 可變形體塊體之建立 9 3.1.2 封閉曲面概念 10 3.1.3 基本接觸類型 12 3.1.4 十一種接觸組合 12 3.1.5 向量式有限元之柔性多面體系統之運動分析 18 3.2 頂點對面之接觸判斷 22 3.2.1 頂點對面之接觸判斷法則 22 3.2.2 頂點對面之接觸流程 23 3.3 稜邊對稜邊之接觸判斷 24 3.3.1 稜邊對稜邊之接觸判斷法則 24 3.3.2 稜邊對稜邊之接觸流程 29 3.4 元素接觸之入侵量計算 30 3.4.1 頂點對面之入侵量計算 30 3.4.2 稜邊對稜邊之入侵量計算 32 3.5 接觸力之計算與分析 34 3.5.1 接觸力向量 34 3.5.2 摩擦力機制 36 3.5.3 質點運動分析 36 3.5.4 接觸彈簧選取 37 第四章數值模擬與分析 39 4.1 摩擦機制側推驗證 39 4.1.1 正立方體側推(一) 39 4.1.2 正立方體側推(二) 45 4.2 摩擦機制傾斜驗證 50 4.2.1 正立方體傾斜(一) 50 4.2.2 正立方體傾斜(二) 56 4.3 半圓環碰撞 61 4.4 柔性柱體碰撞 65 第五章結論與建議 69 5.1 結論 69 5.2 建議 70 參考文獻 71 附錄 A 三維固體在空間中的運動 74
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指導教授	王仲宇陳詩宏	審核日期	2019-1-30
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