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研究生: 陳忠貴
Chen, Chung-kuei
論文名稱: 應用有限元素法模擬光彈條紋圖像
Simulate Photoelastic Fringe Pattern by Using Finite Element Method
指導教授: 陳元方
Chen, Terry Yuan-Fang
學位類別: 碩士
Master
系所名稱: 工學院 - 機械工程學系
Department of Mechanical Engineering
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 75
中文關鍵詞: 等色線次主應力有限元素法等傾線
外文關鍵詞: Finite Element Method, isoclinics, secondary principle stress, isochromatic
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  • 光彈應力分析是一種很普遍且有很多研究的技術。我們可以透過光彈實驗得到具相同主應力方向點的軌跡,與相同主應力差值點之軌跡,此兩組數據為光彈應力分析中之重要參數。
    本文以有限元素法,模擬模型於受負載及邊界條件作用下,由所得之受力模型應力分佈情況,轉換成光彈實驗中之光強度,以模擬穿透式及散射式光彈之條紋影像,並利用實驗方式來與模擬所得條紋圖像作比較驗證。主要是以有限元素模擬光彈應力分析中,等傾線、等色線及散射式光彈中沿光通過路徑其次主應力方向改變與次主應力方向不變之條紋影像。
    在穿透式光彈條紋的模擬,使用圓盤模型來模擬平面偏光場與圓偏光場皆可得到不錯的結果。在散射式光彈條紋圖像模擬,使用圓盤模型來模擬光彈條紋,設定偏極化方向及觀測角皆為45度,得到的模擬圖像非常趨近於理論解模擬結果,得到不錯的結果。使用L型模型模擬次主應力方向沿光線路徑方向改變的光彈條紋,經實驗所得條紋圖像與模擬所得條紋圖像比對,亦可得到相當吻合的結果。

    The photoelasticity stress analysis is a technology with many researches focus on it. We can acquire the locutions of points with the same principle stress direction and the principle stress difference through the photoelasticity experiments These data are the important parameters in photoelasticity stress analysis.
    The main purpose of this article is using Finite Element Method to simulate the distributions of stress when model subject loadings and boundary conditions, then turn these into the intensities of lights to simulate the fringe patterns of transmission and scattered-light photoelasticity. And compare these results with the patterns of photoelasticity experiments. We use Finite Element Method to simulate the isoclinic and isochromatic patterns of photoelasicity experiments and the fringes while the secondary principle stress varies along the path of light and the secondary principle direction fixed.
    In the simulation of transmission photoelasticity, we use the disk model to simulate Plane Polariscope and Circular Polariscope, then we can get a good result. And in the simulation of scattered-light photoelasticity fringe pattern, we also use the disk model to simulate the fringe pattern. Let the polarization and observation direction to be 45 degrees, then we can get the simulation fringe pattern which is close to the experiment pattern. So the result is good. Using the L shape model to simulate the fringes while the secondary principle stress varies along the path of light, the simulation fringe pattern compare with the experiment pattern, the result is found to be good.

    中文摘要………………………………………………………………Ⅰ 英文摘要………………………………………………………………Ⅱ 致謝……………………………………………………………………III 目錄……………………………………………………………………IV 圖目錄…………………………………………………………………VII 表目錄…………………………………………………………………IX 符號說明…………………………………………………………………X 第一章 緒論 1.1研究背景與目的……………………………………………………1 1.2 文獻回顧……………………………………………………………3 1.3本文架構……………………………………………………………7 第二章 偏光彈性法 2.1 光波理論……………………………………………………………8 2.2偏極光………………………………………………………………9 2.3雙折射材料…………………………………………………………9 2.4 光-應力定律………………………………………………………10 2.5平面偏光場理論……………………………………………………11 2.6 圓偏光場理論……………………………………………………14 2.7 散射式光彈理論…………………………………………………16 2.7.1 簡介……………………………………………………………16 2.7.2 平面偏振光通過未受力模型的散射現象……………………17 2.7.3 次主應力………………………………………………………18 2.7.4 光-應力定律……………………………………………………19 2.7.5 平面偏振光入射時的散射光場………………………………20 2.7.6 次主應力方向改變的光場……………………………………22 第三章 有限元素法 3.1有限元素法簡介……………………………………………………26 3.2二維四邊形元素與形狀函數………………………………………27 3.3自然座標……………………………………………………………30 3.4二維四邊形二次元素………………………………………………31 3.5三維八節點立方體元素……………………………………………32 3.6 三維二十節點立方體元素………………………………………34 第四章 模擬方法與散射光彈實驗系統 4.1 模擬方法………………………………………………………… 36 4.1.1 ANSYS模擬……………………………………………36 4.1.2 形狀函數內差……………………………………… 37 4.2 散射式光彈實驗系統與方法……………………………………39 4.3 影像處理…………………………………………………………42 第五章 模擬、實驗結果與討論 5.1穿透式光彈模擬………………………………………………43 5.2 散射式光彈模擬…………………………………………… 50 5.3 散射式光彈實驗…………………………………………… 60 5.4 討論………………………………………………………… 64 5.4.1 有限元素法………………………………………… 64 5.4.2 次主應力方向改變的散射光場…………………… 65 第六章 結論與建議 6.1結論……………………………………………………………… 67 6.2建議……………………………………………………………… 69 參考文獻………………………………………………………………70

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