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研究生:官志達
研究生(外文):Chih-Ta Kuan
論文名稱:應用DQEM於求解具剪變形之任意複合變斷面樑結構物之振動問題
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:49
中文關鍵詞:數值積分表示微分元素法數值積分表示微分法
外文關鍵詞:DQMDQEM
相關次數:
  • 被引用被引用:4
  • 點閱點閱:152
  • 評分評分:
  • 下載下載:17
  • 收藏至我的研究室書目清單書目收藏:1
數值積分表示微分元素法(DQEM)為一種分析連體力學問題的數值方法。此數值分析法除了能有系統地編成電腦程式外,因其具有較高的耦合特性,且考慮所有的基本條件,故使用較少的離散點就能得到收斂,可有效地求得精確解,大幅降低計算機的運算量。
數值積分有限元素法是將欲分析的結構物分割成有限個元素,再利用數值積分表示微分法的技巧,對定義於各個元素內的統御微分或偏微分方程式,兩個相鄰元素相連接的相鄰邊界上之轉接條件式及領域邊界上之邊界條件式,做數值的離散化。
本篇論文主要是針對I型樑的振動問題做研究,以期望能減少結構物的變形量,並加以分析其振動頻率對結構物的影響。往後的研究方向,就朝向更具體實際的複雜結構物做更好的驗證。
The differential quadrature element method (DQEM) is a numerical analysis method for analyzing continuum mechanics problems. The numerical procedure of this method can systematically implemented into a computer program. The coupling of solutions at discrete points is strong. In addition, all fundamental relations are considered in constructing the overall discrete points, and accurate results can be obtained by using less arithmetic operations which can reduce the computer CPU time required.
Like FEM, in using DQEM to solve a problem the domain is separated into many elements. The DQ discretization is carried out on an element-basis. The discretized governing differential or partial differential equations defined on the elements, transition condition on inter-element boundaries and boundary conditions are assembled to
obtain an overall algebraic system.
In this paper, the DQEM analysis model of nonprismatic I beams resting on elastic foundations is developed, and the related computer problem is implemented. Sample problems of static deformation and free vibration are analyzed. They prove that the developed DQEM analysis
model is excellent.
AbstractⅠ
摘要Ⅱ
誌謝.Ⅲ
目錄..Ⅳ
表目錄Ⅵ
圖目錄Ⅶ
符號表Ⅸ
第一章 緒論
1-1 研究動機1
1-2 文獻回顧2
第二章 數值積分表示微分法(DQM)3
2-1 DQM的簡述3
2-2 DQM的數學模式4
2-3 計算權重係數的方法5
2-3-1 方法一6
2-3-2 方法二7
2-3-3 方法三8
第三章 數值積分表示微分元素法(DQEM)12
3-1 有限元素法(FEM)12
3-2 有限元素法的簡述13
3-3 DQEM的簡述14
3-4 DQEM的求解步驟14
3-5 兩者之間的差別15
第四章 變斷面剪變形樑振動問題模式17
4-1 模型建立17
4-2 I型斷面剪變形懸臂樑34
4-3 I型斷面剪變形FIX-PIN樑37
4-4 I型斷面剪變形FIX-FIX樑40
4-5 I型斷面剪變形簡支樑43

第五章結論46
參考文獻47
附錄一 五個離散點的權重係數一覽表A
附錄二 六個離散點的權重係數一覽表B
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【10】Kukreti, A. R., Farsa, J., and Bert, C. W.,”Differential quadrature and rayleigh-ritz methods to determine the fundamental frequencises of simply supported rectangular plates with linerly varying thickness,” Journal of Sound Vibration, Vol.189, No.1, pp
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