多面塊體數值模擬-塊體的切割

Numerical Simulations for a 3D System Composed of Polyhedral Blocks-Dissection of Polyhedral Blocks

張君豪(Chun-Hao Chang)

指導教授 ： 盛若磐

國立中央大學/工學院/土木工程學系/碩士(2006年)

摘要

多面塊體之數值模擬過程中，除了已知的多面塊體外觀形體(頂點、稜邊、面及座標)輸入值，剩下的體積、慣性積、慣性矩等物理量都需要由電腦程式算出，以便用於後續多面塊體碰撞行為之計算。而多面塊體在計算體積、慣性積、慣性矩時，對於多面塊體的形體無法像計算對稱的物體一樣單純只用對稱軸或是積分方式計算出，因此必須要先對多面塊體切割成數個四面體。藉由Simplex積分法來求得各個最簡積分單元的結果並且加總算出該多面塊體的體積、慣性積、慣性矩。

本論文針對許秀真(2001)的多面塊體模擬程式的塊體切割部分做更進一步的討論；另外提出新的切割方式，利用拋棄三稜頂點與降稜來切割多面體。在不增加新頂點的情況下，切割出的四面體數目甚至比許秀真的切割方法還要少。減少切割數的目的在於減少對單一塊最簡多面體-四面體的物理量之積分運算。最後探討判斷多面塊體切割最少及比較本論文與許秀真的切割結果。

關鍵字

四面體 ； 三角化 ； 拓樸學 ； 多面體

並列摘要

In simulating the mechanical behavior of a polyhedron assembly, the volume and moment of inertia of each polyhedron have to be calculated based on the geometric and material information of each polyhedron. The purpose of this paper is to develop a computer sub-code which gives an efficient and effective way to achieve the goal.

In the developed code, a polyhedron is divided into several tetrahedrons and the calculation of the volume and the moment of inertia of each tetrahedron follows. It is obvious that the less the divided tetrahedrons the less the calculation effort. However, the dissection of a polyhedron takes time too. So, a minimal dissection of a polyhedron may not necessarily be the most efficient choice.

Comparison between two different dissection methods is presented in this paper as well as their dissection algorithms.

並列關鍵字

triangulation ； tetrahedron ； topology ； polyhedron

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