多面塊體系統之運動模擬; Motion Simulations for a System Composed of Polyhedral Blocks

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Title:	多面塊體系統之運動模擬;Motion Simulations for a System Composed of Polyhedral Blocks
Authors:	許秀真;Hsiu-chen Hsu
Contributors:	土木工程研究所
Keywords:	多面塊體;接觸判斷;Simplex積分法;臨界時間步程長;polyhedron;contact detection;Simplex integrati
Date:	2001-06-15
Issue Date:	2009-09-18 17:06:00 (UTC+8)
Publisher:	國立中央大學圖書館
Abstract:	本論文提出可模擬任意形狀之多面塊體系統運動的數值程式。多面塊體間僅須進行頂點對面、稜邊對稜邊兩種型態的接觸判斷即可歸納出正確的接觸型態；並因引入層層篩選可能的接觸組合之多層接觸偵測技巧，故能節省大量的程式運算時間。前人對於任意形狀的多面體體積與慣性張量之計算皆以簡化或假設的方式處理，因而造成在塊體形狀與分析問題上之適用窒礙，藉由Simplex積分法即能求得正確值。最後利用能量與動量之守恆定律加以驗證，驗證相關推導和程式執行之正確性。本研究可以由程式自動將各種多面體切割成最少個最簡積分單元（四面體），亦可自由控制多面體各佔的百分比與幾何形狀，在空間中自由生成，並利用AutoCAD與PhotoImpact製作動畫軟體展現出塊體的整體運動過程，以利觀察分析。由程式模擬結果顯示，藉由頂點對面、稜邊對稜邊兩種接觸判斷即能正確判斷出各種形式的接觸型態。由於顯性時間積分法為條件性數值收斂，故時間步程長須小於一臨界值才能確保數值穩定。本論文針對不同多面體質量與接觸彈簧勁度值進行參數研究，結果顯示可利用估算臨界時間步程長。 In this thesis, a new algorithm and a computer code are developed for numerical simulations of a system composed of polyhedron of any shape, which can undergo arbitrary large motions and rotations. Only the contact type of vertex-to-face and edge-to-edge are required for detect although a total of six types of contacts are theoretically possible between any two polyhedral blocks. In addition, the contact system decomposed into contact hierarchies is used for trivial rejection of contact. In consequence, program time can be speeded up. Difficulties and complexities of computation of volume and inertial tensor of polyhedron of any shape are able to solved by the Simplex integration method. The number of each type of polyhedron used in the code can be designed by the analyst. Simulation results can be linked with the commercial code such as AutoCAD and PhotoImpact to display the distribution of blocks in space. From the results of simulation, it is found that all type of contacts between blocks can be well detected. The mutual reactions among elements are taken account by the relative forces and contact through normal and tangential spring model. The explicit time integration scheme is applied to solve the dynamic equations of each block. The explicit time integration algorithm is only numerically stable if the timestep is less than the critical timestep. Parameter studies of the influence of mass of block and spring stiffness on the estimation of critical timestep are conducted in this thesis.
Appears in Collections:	[Graduate Institute of Civil Engineering] Electronic Thesis & Dissertation

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