 |
|
|
|
以作者查詢圖書館館藏 、以作者查詢臺灣博碩士 、以作者查詢全國書目 、勘誤回報 、線上人數：12 、訪客IP：3.128.30.45
姓名 李世昌(Shih-chang Lee) 查詢紙本館藏 畢業系所 土木工程學系 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)相關論文 檔案 [Endnote RIS 格式]
[相關文章]
[文章引用]
[完整記錄]
[館藏目錄]
[檢視]
- 本電子論文使用權限為同意立即開放。
- 已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
- 請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。
摘要(中) 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。摘要(英) 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.關鍵字(中) ★ 塊體形狀
★ 旋轉矩陣
★ 接觸判斷關鍵字(英) ★ shape of polyhedral block
★ contact detection
★ rotation matrix論文目次 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.........................................90參考文獻 1. Cundall, P. A., “Formulation of Three-dimensional Distinct Element Model—PartⅠ. 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. Das, B.M., Principle of Soil Dynamics, PWS-KENT, Boston, USA, pp. 5-51 (1993).
5. Oldenburg, M. and L. Nilsson, “The Position Code Algorithm for Contact Searching,” Int. J. Numer. Meth. Engng., Vol. 37, pp. 359-368 (1994).
6. 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).
7. Vaid, Y. P. and J. C. Chern, “Cyclic and Montonic Undrained Response of Saturate Sands,” Advances in the Art of Testing Soils under Cyclic Conditions, pp. 120-147 (1985)
8. Wang, S.P. and E. Nakamachi, “The Inside-Outside Contact Search Algorithm,” Int. J. Numer. Meth. Engng., Vol. 40, pp. 3665-685(1997).
9. Zhong, Z.H. and L. Nilsson, “A Contact Searching Algorithm for General 3-D Contact-Impact Problems,” Computers and Structures, Vol. 34, No. 2, pp.327-335 (1990).
10. Ng, T.-T. and X. Lin, “Numerical Simulations of Naturally Deposited Granular Soil with Ellipsoidal Elements,” Proceedings of the 2nd Int. Conference on DEM, IESL Publications, pp. 557-567 (1993)
11. Ng, T.-T. and X. Lin, “Short Communication Contact Detection Algorithms for Three Dimensional Ellipsoids in Discrete Element Modelling,” International Journal forNumerical and Analytical Methods in Geomechanics, vol. 19, pp. 653-659 (1995)
12. Ng, T.-T. and E. Petrakis, “Small-Strain Response of Spheres Using Discrete Element Method,” Journal of Engineering Mechenics, ASCE, Vol. 122, No. 3, pp. 239-244 (1996)
13. Rothenburg, L. and R. J. Bathurst, “Analytical Study of Induced Anisotropy in Idealied Granular Materials,” Geotechnique, Vol. 39, No. 4, pp. 601-614 (1989).
14. Rothenburg, L. and R. J. Bathurst, “Numerical Simulation of Idealized Granular Assemblies With Plane Elliptical Particles,” Computers and Geotechnics, Vol. 11, pp. 315-329 (1991)
15. Rothenburg, L. and R. J. Bathurst, “Micromechanical Features of Granular Assemblies With Planar Elliptical Particles,” Geotechnique, Vol. 42, No. 1, pp. 79-95 (1992)
16. Lin, J.S., and S. Chen, “Discrete Element Modeling of Direct Shear and Simple Shear Tests,” Proceedings of 2nd Int. Conference on DEM, IESL Publications, pp. 245-252 (1993).
17. Wang, C.Y. and V.C., Liang, “A Packing Generation Scheme for the Granular Assemblies with Planar Elliptical Particle,” International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 21, pp. 347-358 (1997).
18. Tran, T. X. and R. B. Nelson, “Analysis of Disjoint Two-Dimensional Particle Assemblies.” Journal of Engineering Mechenics, ASCE, Vol. 122, No. 12, pp. 1139-1148 (1996)
19. 王泉博，「二維圓磐顆粒之堆積模擬與應用」，碩士論文，國立中央大學土木工程系，中壢(1996)
20. 李宗龍，「橢圓顆粒介質體運動之數值模擬」，碩士論文，國立中央大學土木工程系，中壢(1997)。
21. 李承恩，「三維球形顆粒介質體變形分析」，碩士論文，國立中央大學土木工程系，中壢(1997)。
22. 莊清鏘，「二維可變形多體系統的動、靜態分析」，博士論文，國立中央大學土木工程系，中壢(1999)。
23. 劉建宏，「橢球顆粒介質體運動之數值模擬」，碩士論文，國立中央大學土木工程系，中壢(1998)。
24. 陳俊全，「混合型橢球顆粒介質體運動之數值模擬」，碩士論文，國立中央大學土木工程系，中壢(1999)。
25. 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)。
26. 鄭凱文，「三維顆粒介質與變形體互制行為之數值模擬」，碩士論文，國立中央大學土木工程系，中壢(2003)。
27. Argyris, J.,“An Excursion Into Large Rotations,”Computer Methods In Applied Mechanics And Engineering, Vol. 32, pp. 85-155, (1982).
28. Zhao, H., “The Virtual Contact Loading Method for Contact Problems Considering Material and Geometric Nonlinearities,” Computers and Structures, Vol. 58, No. 3, pp. 621-632 (1996).
29. 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 盛若磐(Jopan Sheng) 審核日期 2003-7-17 推文 plurk
funp
live
udn
HD
myshare
netvibes
friend
youpush
delicious
baidu
網路書籤 Google bookmarks
del.icio.us
hemidemi
facebook
twitter
google
reddit