織品布料之動態模擬

Abstract

本論文之內容為模擬國旗飄揚的動態過程，主要是結合有限單元分析、動態方程式、影像處理等基礎來完成。環境設定為旗面沿風的切線方向產生小變形的擺動，不考慮流場的影響，純粹以受載的形式、方向、大小來調整旗面的變化。 以有限單元分割國旗，網格採四角單元，結構體的形式採薄膜加薄板的組合結構，節點考慮五個自由度，分別是XYZ三軸的位移變化及XY軸的旋轉量，並且引入ID Array來計算自由度的編號，以及代入Band Matrix解矩陣。使用的動態方程式為隱式直接積分法，因為布料之阻抗效果不明顯，所以在此不考慮阻抗的效果。電腦繪圖的部分需以2D之畫面展示3D的立體效果，以及降低馬克光帶效應的影響和前後覆蓋的問題。

The goal of this thesis is the dynamic simulation of a flying national flag. It is accomplished on the bases of finite element analysis, dynamic equation, and computer graphics. The wind influence on flag is imposed through only vertical component since the flag is always flying tangential to the wind. We model the flag with rectangular plate elements which is a combination of the plane stress and the plate bending element. Every node has five degree of freedom (displacement of X, Y, and Z direction, rotation of X, Y axis). We also use ID-Array to compute the degree of freedom, and apply Band-Matrix to solve for the answer. For dynamic simulation, we use Implicit Direct Integration Method. Because the flag does not have much bending resistance, we do not consider the damp-matrix [C]. On the part of computer Graphic, we show the effect of 3D simulation with frames of 2D, eliminate the Mach Band Effect, and solve the question of covering.