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。

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.

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