離散元素法(Discrete Element Method, DEM)在近年來已逐漸地使用在多種科學領域的分析中，然由於要有效探求一些顆粒介質體的真實行為時，往往需要以大量的顆粒進行模擬。而在此模擬分析過程中，卻常常面臨一個嚴重且困難的問題，亦即耗費的計算時間過久，而花費的時間中又以接觸判斷最為費時。因此本論文針對此一問題提出縮短接觸判斷流程、快速搜尋判斷的方法，提供相關研究者一個具體可行的方式，在顆粒數量龐大時，將可有效地縮短數值分析時間。 此外，離散元素法在模擬一些離散介質體系，往往需要以一些相異顆粒來組成分析模型，而過去在此類分析過程中，顆粒間碰撞彈簧、阻尼和時間增量數值的選取方式並無定則，特別是對於不同大小、材料性質相異之顆粒碰撞問題時，經常以經驗值來計算，造成相當大之分析誤差。本論文亦將針對此問題，提出一個具體可行的方式，可有效地模擬三維彈性圓球顆粒正向碰撞行為，並進而推導出顆粒介質體之速度合成分析法及一套運算系統，可應用到多球顆粒系統之分析。本論文所提各項方法之精確度及可行性，可透過一系列例題之演算得到驗證。 The discrete element method (DEM) has been widely used in various scientific fields to simulate the behavior of particle conjectured medium. However, a lot of computation time has to be spent especially for the contact searching and detection of particles, if large amount of particles are used for the simulation. This thesis proposes a fast contact searching scheme which can reduce the computation time dramatically compared with conventional scheme in DEM. When applied in simulating the behavior of granular assemblies, Discrete Element Method (DEM) usually need different particles to assemble analysis model. However, the determination of the values of the stiffness of normal contact spring, damping coefficient, and time steps size are still based on experience rule since the past decades. Certain amount of error would be accumulated and then leads to an inaccurate behavior prediction. In this thesis, a nonlinear normal impact analysis method is presented to simulate the dynamic behaviors of particles with different sizes and material properties. Besides, the so called “velocity summation method” is developed further to simulate the behavior of multi-particles. The accuracy and efficiency of all the proposed methods are demonstrated and verified through some benchmark problems.
