J4  2011, Vol. 45 Issue (4): 650-655    DOI: 10.3785/j.issn.1008-973X.2011.04.010
 自动化技术、电信技术

1.浙江大学 CAD&CG国家重点实验室,浙江 杭州 310027； 2.台州学院 机械工程系,浙江 台州 318000
Algorithm with hybrid method based for sphere packing in
two-dimensional region
FANG Xi-wu1,2, LIU Zhen-yu1, TAN Jian-rong1
1. State Key Laboratory of CAD&CG, Zhejiang University, Hangzhou 310027, China;
2. School of Mechanical Engineering, Taizhou University, Taizhou 318000, China
 全文: PDF  HTML

Abstract:

A new hybrid method was proposed for sphere packing in two-dimensional region, which combined the traditional dynamic method with the traditional constructive method. The algorithm calculated the particles’moving directions with two different methods according to the two different touching objectives during the process of falling. When the touching objective was particle, the moving direction was calculated with the purely geometric-based method in which the new direction was downward along the tangential direction of the two-contact particles’ touching point. The moving direction of the particle approximated the physical law of the dynamic method. When the touching objective was the boundary of the container, the new direction was calculated with the elastic collision theory, which consisted with the physical law of the dynamic method. The touch detections between particles were based on the advancing-front elements of the constructive method. The time to create the granular particles set was linear with the particle number, and this process was completed in a comparatively short time with high density particles set.

 : TP 391.9

 ［1］ WEBB M D, LEE DAVIS I. Random particle packing with large particle size variations using reduceddimension algorithms ［J］. Powder Technology,2006,167(1): 10-19. ［2］ FENG Y T, HAN K, OWEN D R J. Filling domains with disks: an advancing front approach ［J］. International Journal for Numerical Methods in Engineering, 2003, 56(5): 699-713. ［3］ HAN K, FENG Y T, OWEN D R J. Sphere packing with a geometric based compression algorithm ［J］.Powder Technology, 2005, 155(1): 33-41. ［4］ BAGI K. An algorithm to generate random dense arrangements for discrete element simulations of granular assemblies ［J］.Granular Matter, 2005, 7(1): 31-43. ［5］ MUNJIZA A, ANDREWS K R F. NBS contact detection algorithm for bodies of similar size ［J］. International Journal for Numerical Methods in Engineering, 1998, 43(1): 131-149. ［6］ NEZAMI E G, HASHASH Y M A, ZHAO Dawei, et al. A fast contact detection algorithm for 3D discrete element method ［J］.Computers and Geotechnics, 2004, 31(7): 575-587. ［7］ PSCHEL T, SCHWAGER T. Computational granular dynamics: models and algorithms $M$. Berlin: Springer, 2005. ［8］ GENSANE T, RYCKELYNCK P. Producing dense packings of cubes ［J］. Discrete Mathematics, 2008, 308(22): 5230-5245. ［9］ BAGI K. A quasistatic numerical model for microlevel analysis of granular assemblies ［J］. Mechanics of Materials, 1993, 16(1/2): 101-110. ［10］ THOMAS P. Discontinuous deformation analysis of particulate media ［D］. Berkeley: University of California, 1997. ［11］ LIN X, NG T. A threedimensional discrete element model using arrays of ellipsoids ［J］. Geotechnique, 1997, 47(2): 319-329. ［12］ SAKAGUCHI H, MURAKAMI A. Initial packing in discrete element modeling ［M］∥Discrete element methods: numerical modeling of discontinua: proceedings of the 3rd international conference on discrete element methods. Tokyo: ［s.n.］, 2002. ［13］ SULLIVAN C O. The application of discrete element modelling to finite deformation problems in geomechanics ［D］. Berkeley: University of California, 2002. ［14］ ELHAMALAWI A. A 2D combined advancing frontDelaunay mesh generation scheme ［J］. Finite Elements in Analysis and Design, 2004, 40(9/10): 967-989. ［15］ WANG W X, MING C Y, LO S H. Generation of triangular mesh with specified size by circle packing ［J］. Advances in Engineering Software, 2007, 38(2): 133-142. ［16］ BENABBOUA A, BOROUCHAKIA H, LAUGA P, et al. Numerical modeling of nanostructured materials finite elements in analysis and design ［J］. Application to Nanostructures, 2010, 46(1/2): 165-180. ［17］ BENABBOU A, BOROUCHAKI H, LAUG P, et al. Geometrical modeling of granular structures in two and three dimensions ［J］. International Journal for Numerical Methods in Engineering, 2009, 80(4): 425-454. ［18］ FERREZ J A. Dynamic triangulations for efficient 3D simulation of granular materials ［D］. Switzerland: Ecole Polytechnique Federal de Lausanne, 2001.