本研究以蒙特卡羅法為模擬顆粒群體行為的基礎，並配合模擬退火法作為壓密機制的核心策略，建構了橢球隨機緊密堆積的模擬系統。
除了基本的壓密機制外，本研究並設計了兩種策略以在演算過程中儘量維持顆粒在試體中排列的均勻度。一項策略為「顆粒優先抽取序列」，可使試體中鬆散區域的顆粒有較高機率被調整姿態和位置；另一項策略為「上下移動最大步幅對調」，可使試體中緊密區域的顆粒往鬆散區域移動。
針對數百顆、任意形狀和大小的橢球群，本系統可產生密度甚高的堆積試體。其中正球隨機堆積平均密度曾達73.19%，超過已知文獻，接近體心、面心堆積的74.05%。系統模擬顆粒形狀近似鋼珠、M&M’s巧克力、豐浦標準砂等堆積時，其試體所量得的密度均超過真實實驗試體。
研究觀察到極緊密的堆積試體中，接觸數分布狀況呈現雙峰曲線，是其他文獻中未見到之現象。
顆粒形狀一直是影響堆積密度的重要因子。本研究觀察到稍微偏離正球形的橢球，其堆積密度顯著上升，而偏離程度超過某一界線後開始下降，此結論與Donev[7]一致。在各種形狀的單一種類堆積模擬中，發現三軸長0.427、0.315、0.263的形狀可以達到最高的密度。該試體經300萬回合的搖晃後，密度可達73.11%。在平均接觸數方面，研究亦發現以正球形為最低，形狀偏離正球形即顯著上升。

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].

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