卵形顆粒介質運動之數值模擬

Numerical Simulations for Granular Assemblies with 3D Egg-shaped Particles

林昇鴻(Sheng-Hung Lin)

指導教授 ： 王仲宇 ； 盛若磐

國立中央大學/工學院/土木工程學系/碩士(2006年)

摘要

本論文提出模擬三維顆粒動態行為的數值模擬程式，顆粒形狀包括卵形顆粒及長、扁橢球顆粒。新發展出的卵形顆粒之形狀是利用四圓弧逼近法及座標旋轉的觀念，顆粒間的接觸判斷分成球面、曲面接觸為主，以加快程式運算速度；程式驗證利用能量與動量守恆定律加以證明程式執行之正確性。
於程式中可在有限空間生成不同形狀之顆粒，霣降、堆積後進行安息角試驗模擬，以 MATLAB 7.1 軟體作為後處理，可展現出顆粒在空間的運動狀況、分佈情況與剖面圖，以利分析。
孔隙比、顆粒間之接觸點數、顆粒形狀、顆粒基本摩擦角等堆積體有關參數，為影響顆粒狀材料力學行為之重要因素。本論文針對不同顆粒形狀與安息角的關係做研究，安息角試驗方式分為移除單一邊牆與單一邊牆斜傾90度兩種，依試驗分析結果得知，顆粒形狀確實會影響顆粒堆積體安息角之大小，且扁橢球的安息角最大，卵球次之，長橢球最小。

關鍵字

安息角 ； 顆粒材料 ； 卵形顆粒 ； 扁橢球 ； 接觸行為 ； 堆積

並列摘要

In this thesis, a new algorithm and a computer code are developed for 3D numerical simulations of granular assemblies composed of egg-shaped particles, ellipsoidal particles and long ellipsoidal particles. The newly developed egg-shaped particles are designed by the revolution of an ellipse, formed by four connected arcs, about the major axis passing through its centroid in order to speed up the process of algorithm. Coordinates of the centroid, directions of the major axis and lengths of major and minor axes are the essential data for the packing generation and associated contact detection.

The domain to be filled with particles can be a polyhedron of any shape. Simulation results can be processed by MATLAB 7.1 to display the distribution of particles in space and the fabric structure at any instant. Parameter studies of the influence of the void ration, the contact numbers among the gravels, particle shape and the internal friction angle between particles on the macroscopic behaviors of particles assemblies are conducted in this thesis. In this study, it emphasizes the relationship between the angle of repose and the particle shape. The reactions of angle of repose are taken account by the relative particle shape through remove one side of wall and set a wall spinning slowly into 90 degree. It is found that the particle shape will influence the angle of repose, ellipsoidal particles are the most, and then egg-shaped particles and the long ellipsoidal particles are the least.

並列關鍵字

angle of repose ； contact behavior ； ellipsoidal particle ； granule material ； egg-shaped particle ； packing

參考文獻

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