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研究生:楊禮龍
論文名稱:薄殼結構在位移負荷作用下之幾何非線性分析
論文名稱(外文):Geometrically Nonlinear Analysis of Thin Shell Structures under Displacement Type Loading
指導教授:蕭國模
學位類別:碩士
校院名稱:國立交通大學
系所名稱:機械工程系所
學門:工程學門
學類:機械工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:95
語文別:中文
論文頁數:100
中文關鍵詞:薄殼結構位移負荷幾何非線性分析共旋轉法增量迭代法
外文關鍵詞:thin shell elementdisplacement loadinggeometrically nonlinear analysisco-rotational finite element formulationincremental-iterative method
相關次數:
  • 被引用被引用:6
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  • 下載下載:41
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本文以共旋轉(co-rotational formulation)有限元素推導法及增量迭代法來探討薄殼結構在位移負荷作用下的幾何非線性行為。
本文採用文獻[24]提出的平面三角殼元素,此元素是由CST(constant strain triangle) 平面元素與DKT(discrete Kirchhoff theory)三角板元素疊加而成。此元素有三個節點,每一節點具有六個自由度。結構的節點座標、增量位移與增量旋轉、以及結構的平衡方程式都是定義在一組固定的總體座標系統上;而殼元素的應變、節點內力以及元素剛度矩陣,則是在當前元素位置上建立的元素座標上定義。
本文採用牛頓-拉福森(Newton-Raphson)法和弧長控制(are length control)法的增量迭代法來解受位移負荷之結構的非線性平衡方程式。
最後,本研究以四個數值例題探討殼結構受到各種位移負荷之幾何非線性行為。例題一為鉸接球殼受到不同的側向位移負荷,例題二為圓柱殼受到不同的側向位移負荷,例題三為含缺口之簡支圓柱殼之邊界受到均勻位移及均勻力負荷,例題四為懸臂板受到不同的側向位移負荷。由例題結果可以知道結構受單一位移負荷及力負荷時,其平衡路徑是一樣的,但受多個位移負荷作用與受多個力負荷作用時,結構的行為有很大的差異。
The geometrically nonlinear behavior of thin shell structure under displacement loading are investigated using the co-rotational finite element formulation and a incremental-iterative method.
The shell element employed here is the flat three-node triangular shell element with six degrees-of-freedom per node proposed by Bathe and Ho’s [24] .The shell element is obtained by superimposing CST(constant strain triangle)element and DKT(discrete Kirchhoff theory) triangular plate element. The nodal coordinates, displacements, rotations, and the equilibrium equations of the structure are defined in a fixed global set of coordinates. The strains of shell element, the element internal nodal forces, the element stiffness matrix are defined in terms of element coordinates, which are constructed at the current configuration of the shell element.
A incremental-iterative method based on the Newton-Raphson method and constant arc length method is used for solving nonlinear equilibrium equations with displacement loading.
Four numerical examples are studied to investigate the geometrically nonlinear behavior of thin shell structures under different proportional displacement loadings. Example 1 is a hinged spherical shell under different lateral displacement loadings, Example 2 is a cylindrical shell under different lateral displacement loadings, Example 3 is a simply supported cylindrical shell with cutout under uniform in plane displacement loadings and force loadings, Example 4 is a cantilever plate under different lateral displacement loadings. It is found that a single concentrated displacement loading is equivalent to a single concentrated force loading as expected. However, the difference between the structure behaviors correspond to multiple displacement loading and force loading is remarked.
中文摘要 …………………………………………………………….. I
英文摘要 …………………………………………………………….. II
致謝 ……………………………………………………………………. IV
目錄 ………………………………………………………………….. V
圖目錄 ………………………………………………………………. VI
第一章 緒論 ………………………………………………………… 1
第二章 理論推導 …………………………………………………….. 3
2.1 基本假設 ……………………………………………………. 3
2.2 座標系統 ……………………………………………………. 3
2.3 旋轉向量 ………….……………………..………………….. 4
2.4殼元素變形的描述 .…………………………………………. 4
2.4.1常應變三角元素(CST)的變形描述 ……………………. 5
2.4.2 DKT元素的變形描述 .………………………………… 7
2.5元素內力與元素剛度矩陣 …………………………………… 10
2.5.1 CST元素之節點內力與剛度矩陣 ………………………. 11
2.5.2 DKT元素的節點內力及剛度矩陣 ……………………… 12
2.6元素幾何剛度矩陣 …………………………………………... 13
2.7元素變形角的描述 …………………………………………... 14
2.8系統的平衡方程式與收斂準則 …………………………….. 16
第三章 數值計算方法與程序 ……………………………………… 18
3.1增量迭代法 ………………………………………………….. 18
3.2弧長控制法 ………………………………………………….. 21
3.3數值程序 …………………………………………………….. 21
第四章 數值例題與結果 .……………………………………….….. 23
第五章 結論 ….……...……………………………………………… 30
參考文獻 .…………………………………………………………….. 31
附錄A DKT元素的形狀函數 …………………………………….. 35
附錄B CST元素的剛度矩陣 …………………………………….. 41
附錄C 分佈反力之節點值與節點反力的關係 ……………………. 42
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