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研究生:王俊富
研究生(外文):Chun-Fu Wang
論文名稱:應用DQEM離散法及EDQ時間積分法於求解具剪變形之軸對稱複合圓板的動態反應
指導教授:陳長鈕
指導教授(外文):Chang-New Chen
學位類別:碩士
校院名稱:國立成功大學
系所名稱:造船及船舶機械工程學系
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:2002
畢業學年度:90
語文別:中文
論文頁數:54
中文關鍵詞:軸對稱複合圓板數值積分表示微分法延伸式數值積分表示微分
外文關鍵詞:DQEMEDQDQM
相關次數:
  • 被引用被引用:3
  • 點閱點閱:119
  • 評分評分:
  • 下載下載:10
  • 收藏至我的研究室書目清單書目收藏:0
摘 要
本論文主要是採用數值積分表示微分元素法(Differential Quadrature Element Method,DQEM)針對軸對稱複合圓板,將求解出來的質量矩陣、和勁度矩陣再應用延展式數值積分表示微分法(Extended Differential Quadrature,EDQ)中的時間積分法來求解複合圓板的動態反應。
起初利用DQ的方法去離散每一個元素上的統御方程式,並利用連接條件定義每一個元素內部的邊界。它是數值積分表示微分元素法的分析模型。
選用EDQ時間積分法來解動態的平衡方程式。其中有發展出兩種不同的演算法,為時間元素對時間元素的積分演算法和Stages by Stages 積分演算法。本論文則採用時間元素對時間元素積分演算法分析軸對稱複合圓板動態反應。
ABSTRACT
This paper uses differential quadrature element method (DQEM) to solve axisymmetric isotropic composite circular plates. The dynamic response can be solved by extended differential quadrature (EDQ) time integration method.
The approach uses the differential quadrature to discretize the governing equations defined on each element, the transition conditions defined on the inter-element boundary. It is a differential quadrature element method analysis model.
The time integration method adopting the extended differential quadrature is used to solve the dynamic equilibrium equation. There are two different approaches for developing the integration algorithms. There ara time-element by time-element integration algorithms and stages by stages integration algorithms. This paper uses time-element by time-element integration algorithms to solve dynamic response.
目 錄
ABSTRACT………………………………………………Ⅰ
摘要……………………………………………………Ⅱ
致謝……………………………………………………Ⅲ
目錄……………………………………………………Ⅳ
表目錄…………………………………………………Ⅵ
圖目錄…………………………………………………Ⅶ
符號說明………………………………………………Ⅷ
第一章 緒論……………………………………… 1
第二章 數值積分表示微分法與數值積分表示微分元素法………6
2-1數值積分表示微分法(DQM)…………………………………… 6
2-2DQ的數學模型…………………………………………7
2-3權重係數的計算方法……………………………………………… 9
2-3-1 應用多項式的一般型求權重係數…………………………9
2-3-2 應用Legendre多項式求權重係數………………………12
2-3-3 應用Lagrange內差多項式來求權重係數………………14
2-4 數值積分表示微分元素法…………………………………………18
第三章 延展式數值積分表示微分(Extended DQ)……………………………20
3-1 Extended Differential Quadrature之離散化………………………20
3-2 EDQ權重係數的計算方法…………………………………………21
3-2-1 應用變函數的內差函數來求解…………………………21
3-2-2 應用適當的解析函數求解…………………………………22
第四章 具剪變形之軸對稱複合圓板動態分析…………………………………23
4-1 模型建立……………………………………………………………23
4-2 應用DQEM離散化……………………………………………………24
4-3 應用EDQ時間積分法求解動態反應………………………………37
第五章 數值分析與模擬…………………………………………………………40
5-1 數值模型……………………………………………………………40
5-2 數值分析計算流程…………………………………………………44
5-3 結果討論……………………………………………………………45
第六章 結論………………………………………………………………………50
參考文獻……………………………………………………………………………51
附錄A 剪力修正係數……………………………………………………………A
附錄B 一階到四階取離散點三的權重係數……………………………………B
附錄C 一階到四階取離散點五的權重係數……………………………………C
附錄D 一階到四階取離散點七的權重係數……………………………………D
附錄E 一階到四階取離散點九的權重係數……………………………………F
附錄F 一階到四階取離散點十一的權重係數…………………………………H
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