Maximum packing densities of basic 3D objects  

作　　者：LI ShuiXiang ZHAO Jian LU Peng XIE Yu 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, China

出　　处：《Chinese Science Bulletin》2010年第2期114-119,共6页

基　　金：supported by the National Natural Science Foundation of China (Grant No.10772005);National Basic Research Program of China (Grant No. 2007CB714603)

摘　　要：Numerical simulation results show that the upper bound order of random packing densities of basic 3D objects is cube (0.78) > ellipsoid (0.74) > cylinder (0.72) > spherocylinder (0.69) > tetrahedron (0.68) > cone (0.67) > sphere (0.64), while the upper bound order of ordered packing densities of basic 3D objects is cube (1.0) > cylinder and spherocylinder (0.9069) > cone (0.7854) > tetrahedron (0.7820) > ellipsoid (0.7707) > sphere (0.7405); these two orders are significantly different. The random packing densities of ellipsoid, cylinder, spherocylinder, tetrahedron and cone are closely related to their shapes. The optimal aspect ratios of these objects which give the highest packing densities are ellipsoid (axes ratio = 0.8:1:1.25), cylinder (height/diameter = 0.9), spherocylinder (height of cylinder part/diameter = 0.35), tetrahedron (regular tetrahedron) and cone (height/bottom diameter = 0.8).Numerical simulation results show that the upper bound order of random packing densities of basic 3D objects is cube （0.78） 〉 ellipsoid （0.74） 〉 cylinder （0.72） 〉 spherocylinder （0.69） 〉 tetrahedron （0.68） 〉 cone （0.67） 〉 sphere （0.64）, while the upper bound order of ordered packing densities of basic 3D objects is cube （1.0） 〉 cylinder and spherocylinder （0.9069） 〉 cone （0.7854） 〉 tetrahedron （0.7820） 〉 ellipsoid （0.7707） 〉 sphere （0.7405）; these two orders are significantly different. The random packing densities of ellipsoid, cylinder, spherocylinder, tetrahedron and cone are closely related to their shapes. The optimal aspect ratios of these objects which give the highest packing densities are ellipsoid （axes ratio = 0.8 ： 1 ： 1.25）, cylinder （height/diameter = 0.9）, spherocylinder （height of cylinder part/diameter = 0.35）, tetrahedron （regular tetrahedron） and cone （height/bottom diameter = 0.8）.

关 键 词：三维物体 堆积密度 随机堆积 四面体 数值模拟 封装密度 立方体 圆柱体 

分 类 号：O123.2[理学—数学] TP391.41[理学—基础数学]