# 臺灣博碩士論文加值系統

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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 IAbstract II誌謝 III目錄 IV表目錄 V圖目錄 VI第一章 緒論 11.1 前言 11.2 無元素法的發展與文獻回顧 21.3 本文架構 3第二章 理論基礎 52.1 剪應變形平板挫屈理論 52.2邊界條件 102.3 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 194.1 方形板計算精度與收斂性分析 194.2四邊簡支承板受單軸壓力、雙軸壓力及剪力 204.3兩邊簡支承，另兩邊固定端板受單軸壓力、雙軸壓力及剪力 214.4三邊簡支承，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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 1 微分再生核近似法於二維平板挫屈之分析 2 受束制之移動最小二乘法在Mindlin平板分析之應用 3 Hermitetype之移動最小二乘法在板、梁分析上之應用 4 基於狀態變數與Hermite型近似之移動最小二乘法在古典板之應用 5 受束制之移動最小二乘法在古典板上之應用 6 齊次基底移動最小二乘法在平板分析上之應用 7 齊次基底移動最小二乘法在複合桿件扭轉上之應用 8 基於狀態變數與Hermite型置點法之移動最小二乘法求解波松問題 9 基於狀態變數與Hermite型置點法之移動最小二乘法在二維彈性力學之應用 10 以受束制之移動最小二乘法求解柏松方程式 11 齊次基底移動最小二乘法在二維彈性力學上之應用

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