Ellipsoid packing simulations

• Main Authors: Way-en Huang, 黃偉恩
• Other Authors: Yu-sin Lee
• Format: Others
• Language: zh-TW
• Published: 2009
• Online Access: http://ndltd.ncl.edu.tw/handle/63917269143100038948

碩士 === 國立成功大學 === 土木工程學系碩博士班 === 97 === This thesis presents a Monte Carlo-based simulation method for the dense packing of 3-dimensional ellipsoids. After generating a container and a set of ellipsoidal particles, the system repeatedly adjusts the locations and attitudes of the particles, one at a time, with a method derived from the simulated annealing heuristic. Maintaining homogeneity is crucial for a set of ellipsoids to reach high density in a simulation, and two strategies are developed for this purpose. The simulation process uses a priority list such that particles located at looser areas are given higher probability to be chosen as the next one to be adjusted. The list is maintained with an effective and efficient method so that it always reflects changes in the particle set. Another strategy is to reverse the condensation direction for a few iterations once in a while, to un-lock dense pockets. This work resulted in a simulation system that is able to pack several hundred particles into very high density. Experiments with identical spheres reach a density of 73.19% approaches the theoretical bound of 74.05%, and is significantly higher than any published simulation or lab result. Shapes mimicing M&M’s�� milk chocolate and Toyoura sand also exceeded those seen in the literature. Extensive computational testing indicated that the contact number distribution becomes double-peaked at high densities, which has never been reported in the literature. Using this system as a tool, we investigated how the shape affects packing among uniform particles. We observed that density is lowest with spheres, increases rapidly when the ellopsoids deviate from the sphere, and decreases again when shapes become extreme. Average contact number also follows a similar trend. These results agree with those of Donev[7].