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研究生: 吳梓瑋
Wu, Tzu-Wei
論文名稱: 應用移動最小二乘法於圓柱體薄殼大變形分析
Application of moving least square method for large deformation analysis of the circular cylindrical shells
指導教授: 王永明
Wang, Yung-Ming
學位類別: 碩士
Master
系所名稱: 工學院 - 土木工程學系
Department of Civil Engineering
論文出版年: 2015
畢業學年度: 103
語文別: 中文
論文頁數: 89
中文關鍵詞: 大變形分析一階剪切變形理論移動最小二乘法圓柱薄殼
外文關鍵詞: Theory of large deformation, Moving least square, Theory of first-order shear deformation
相關次數: 點閱:109下載:5
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  • 本文以一階剪力變形與虛功原理推導控制方程式,據以分析圓柱薄殼之大變形,並以Newton-Raphson method將控制方程式進行線性化的疊代,以求解大變形後殼體的行為,而為了數值計算的方便使用quasi-Hermite type formulation以避免將本構關係式展開,並以移動最小二乘法進行求線性化後系統方程式的數值解,也可進一步計算其變形後軸力、彎矩與剪力。透過上述之方法,本文之數值算例分析了開放圓柱殼受彎矩後變形成封閉圓柱殼、兩端固定端之圓柱薄殼受內壓之線性與非線性分析、簡支與懸臂圓柱殼受軸壓力、雙邊鉸支圓柱殼受外壓力產生挫屈之分析,與開放圓柱淺殼之snap through現象。

    In this thesis, the assumption of first-order shear deformation and the principle of virtual work are used to derive the equilibrium equations of the large deformation theory of cylindrical shells. Using the Newton-Raphson iteration method to linearize the non-linear equilibrium equations and analysis the behavior of the shells under large deformation. In the numerical process, using quasi-Hermite type formulation and moving least squares method, can solve equilibrium equations, constitutive relations and to obtain the numerical solution. With these process, the resulting force, bending moments and shears can also be solved.
    The numerical examples include three categories: an opening shell bent to a closed shell by a moment, buckling of cylindrical shells under compression and the snap through phenomenon of cylindrical shells.

    摘要 I Abstract II 致謝 VIII 目錄 IX 圖目錄 XI 符號說明 XIV 第一章 緒論 1 1.1前言 1 1.2文獻回顧 3 1.3 研究方法 7 1.4本文架構 8 第二章 圓柱薄殼之大變型理論推導 9 2.1 參考構形下圓柱薄殼變形的中曲面特性的描述 9 2.2變形後圓柱薄殼之中曲面特性描述 14 2.3 圓柱薄殼大變形的應變分析 18 2.4圓柱薄殼大變形下之平衡方程式 23 2.5 圓柱薄殼大變形合應力與中曲面應變之關係 31 2.6 Newton-Raphson 疊代法用於圓柱殼大變形 34 第三章 移動最小二乘法之理論推導 40 3.1 移動最小二乘法 40 3.2 Quasi-Hermite type formulation 44 3.3 鄰近點與權函數之選取 47 第四章 數值算例 48 4.1 懸臂圓柱淺殼受彎矩 48 4.2兩端固定圓柱殼受內壓 50 4.3 圓柱薄殼之挫屈 55 4.3.1 實例一、雙邊鉸支受圍壓 55 4.3.2 實例二、簡支受軸壓 56 4.3.3 實例三、懸臂受軸壓 57 4.4 開放圓柱淺殼之snap-through 58 第五章 結論 59 文獻回顧 61 圖 64

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