系統識別號 U0026-0808201217590400 論文名稱(中文) 移動最小二乘法在開放圓柱殼挫屈分析上之應用 論文名稱(英文) Buckling Analysis of Open Cylindrical Shells by the Moving Least Square Method 校院名稱 成功大學 系所名稱(中) 土木工程學系碩博士班 系所名稱(英) Department of Civil Engineering 學年度 100 學期 2 出版年 101 研究生(中文) 林榮相 研究生(英文) Rung-Shiang Lin 學號 n66991198 學位類別 碩士 語文別 中文 論文頁數 96頁 口試委員 指導教授-王永明口試委員-吳致平口試委員-胡宣德口試委員-方中 中文關鍵字 移動最小二乘法  剪應變形理論  挫屈分析 英文關鍵字 moving least square method  shear deformation theory  buckling analysis 學科別分類 中文摘要 本文使用移動最小二乘法分析開放圓柱殼之挫屈行為，在本方法中將控制方程式與邊界條件轉成節點位移函數的表達式並納入節點之局部近似函數，採用所有誤差項之最小二乘法，最後組成全域的近似函數，即可建構一離散的特徵值問題，用以求解特徵值與特徵向量，也就是挫屈荷重與位移挫屈模態。 在開放圓柱殼的推導過程中，我們以 的理論為基礎，考慮剪應變變形效應，推導其挫屈控制方程式，並導出四邊簡支承開放圓柱殼在軸壓與圍壓作用下的解析解，並與數值解作比較。 開放圓柱殼的荷重計算精度與結構的曲率半徑、長寬比、寬厚比有很大的關係，結果顯示，曲率半徑較大時則有較佳的計算結果，而寬厚比越大的圓柱殼精度也會越好。 英文摘要 In this paper, we use the moving least squares method to analyze the buckling of an opened cylindrical shell. By express the governing equation and the boundary conditions in terms of nodal displacements and use the moving least squares technique to minimize the residuals that results from the approximation to the field variable as well as that from approximation to the governing equations and the boundary conditions, a global approximation function can be obtained, and a discrete eigenvalue problem can be established. Thus the eigenvalues and corresponding eigenvectors can be determined, which is the buckling load and the corresponding buckling mode. Based on Flügge’s theory of shell, in this paper we include the shear deformation effect to derive the buckling equations of an opened cylindrical shell and obtained some analytical solutions for a simply supported open cylindrical shell under the axial and lateral confining pressure, and compares the result with the numerical solution. The calculation accuracy for the open cylindrical shell has great relations with the radius of curvature, the length-to-width ratio, and the thickness-to-width ratio of the structure. The results show that there are better results for the case with large radius of curvature, and the greater the thickness-to-width ratio of the cylindrical shell is, the better the accuracy will be. 論文目次 摘要 I Abstract II 致謝 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 文獻回顧 2 1.3 本文架構 4 第二章 圓柱殼挫屈分析 5 2.1 開放圓柱殼控制方程式 5 2.2 邊界條件 9 2.3 開放圓柱薄殼解析解 10 第三章 移動最小二乘法之推導 13 第四章 數值算例 23 4.1 精度與收斂性分析 23 4.2 四邊簡支承開放圓柱殼 24 4.3 四邊固定端開放圓柱殼 26 4.4 二邊簡支承二邊固定端開放圓柱殼 26 4.5 扭力作用 27 第五章 結論 29 參考文獻 31 參考文獻 參考文獻 [1]Flügge, W., Stress in shells, Springer-Verlag, New York, 1973. [2]Donnell, L. H., “Thick general shells under general loading”, Journal of Applied Mechanics, Transactions ASME, Vol.56, No.2, pp. 391-394, 1989. 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