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

林鴻(Hung-Lin)

指導教授 ： 王仲宇

國立中央大學/工學院/土木工程學系/碩士(2015年)

摘要

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。

關鍵字

多面體 ； 接觸偵測 ； 四面體化 ； 視窗面法

並列摘要

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.

並列關鍵字

polyhedron ； contact detection ； tetrahedron ； rotating-window-plane

參考文獻

[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)。

[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).