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研究生:莊皓鈞
研究生(外文):Hao-ChunChuang
論文名稱:移動最小二乘法在平板挫屈分析上之應用
論文名稱(外文):Buckling Analysis of Plates by the Moving Least Square Method
指導教授:王永明
指導教授(外文):Yung-Ming Wang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2012
畢業學年度:100
語文別:中文
論文頁數:70
中文關鍵詞:移動最小二乘法無元素法剪應變形平板挫屈理論
外文關鍵詞:Moving Least Squares MethodElement-Free MethodThe shear deformation theory of flat panel buckling
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  • 被引用被引用:1
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本文主要使用移動最小二乘法(moving least square method, MLSM),搭配剪應變形理論來分析二維平板挫屈問題。利用最小二乘法使函數變量、控制方程式以及邊界條件在節點上之殘值達到最小化可建立一數值計算程序以分析平板之挫屈。
數值算例中分析了在簡支承或固定邊界情況下平板承受單軸、雙軸壓力以及剪力下之挫屈荷重。平板尺寸採用長寬比0.5~3、寬厚比0.05~0.15計算所得的挫屈係數配合相對應的挫屈形狀與解析解比較分析其精度。算例分析結果可知近似函數之基底階數提高、長寬比與寬厚比增加,數值解較快收斂至解析解,顯示本文可準確分析厚板之挫屈荷重。

In this paper, we use Moving Least Square Method and shear deformation theory of plates to analyze the buckling of plates. Using the moving least square technique, we attempt to reduce the residuals that results from the approximation to the field variables, the governing equations and the boundary conditions. The process lead to a numerical method to analyze the buckling of plates.
In numerical example, we calculate the buckling lead of a plate with simply supported or clamped edges, and the plate size with aspect ratio of 0.5 to 3,and thickness ratio of 0.05 to 0.15. The buckling coefficient and the corresponding buckling shapes are compared with the analytic solution to validate the accuracy of this method.
The numerical examples show that when the order of base functions, the aspect ratio and thickness ratio increase, the numerical results converge to the analytical solution.Thus, present method can accurately predict the buckling load of a thick plate.

摘要 I
Abstract II
誌謝 III
目錄 IV
表目錄 V
圖目錄 VI
第一章 緒論 1
1.1 前言 1
1.2 無元素法的發展與文獻回顧 2
1.3 本文架構 3
第二章 理論基礎 5
2.1 剪應變形平板挫屈理論 5
2.2邊界條件 10
2.3 平板挫屈解析解 11
第三章 移動最小二乘法之應用 13
第四章 數值分析結果 19
4.1 方形板計算精度與收斂性分析 19
4.2四邊簡支承板受單軸壓力、雙軸壓力及剪力 20
4.3兩邊簡支承,另兩邊固定端板受單軸壓力、雙軸壓力及剪力 21
4.4三邊簡支承,另一邊固定端板受單軸壓力、雙軸壓力及剪力 21
第五章 結論 23
參考文獻 24

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