臺灣博碩士論文加值系統

摘要

近年來DQEM(數值積分表示微分元素法)在陳長鈕老師的開發研究下已成為一種重要的數值結構分析技巧，而且能有系統的編寫成求解的電腦程式。
DQEM(數值積分表示微分元素法)在結構分析上具有高度的數值耦合特性，在分析時所需選取的網格分割點也較少，不但可以降低運算過程中所耗費的時間，並可得到較好的收斂速度和準確性。
本篇論文將應用DQEM(數值積分表示微分元素法)離散法將剪變形樑之統御方程式離散化，並考慮元素內部的連接條件和邊界條件，經總體組合後再使用EDQ(延伸數值積分表示微分法)時間積分法求解具剪變形之樑的動態反應，並應用於數個不同的實例分析以驗證此法的精確性。

Abstract
In recent years, the differential quadrature element method(DQEM) proposed by Dr. C.N. Chen has been an important method for analyzing the structure problems. The numerical procedure of this method can systematically implemented into a computer program.
The coupling of solutions at discrete points is strong by using the differential quadrature element method. Thus, accurate and convergence can be assured by using less discrete points and less arithmetic operations which can reduce the computer CPU time required.
In this work, the DQ discretization of shear deformable bean is carried out on an element-basis. The discretized governing differential equations defined on the elements, transition conditions on inter-element boundaries and boundary conditions are assembled to obtain an overall algebric systems. Then, using the EDQ time integration algorithm to solve the dis-crete equations of motion of structural dynamics problems. Sample problems are analyzed, and prove that the EDQ analysis model is excellent.

目錄
英文摘要 І
摘要 Ⅱ
誌謝 Ⅲ
目錄 Ⅳ
表目錄 Ⅵ
圖目錄 Ⅶ
符號表 Ⅷ
第一章 緒論 1
第二章 數值積分表示微分法(DQM) 3
2.1 DQM介紹 3
2.2 DQM的數學模型 4
2.3 DQEM介紹 5
2.4權重係數的計算方法 7
2.4.1以多項式理論求解 7
2.4.2以Legendre polynomial求解 9
2.4.3以Lagrange interpolated polynomial 求解10

第三章 延伸數值積分表示微分 15
3.1 EDQ介紹 15
3.2 EDQ的數學模型 16
3.3權重係數的計算方 16
3.4對應關係轉換(座標轉換) 18
第四章 應用EDQ發展出來的時間積分法 21
4.1 Time-element by time-element 法 21
4.2 Stage by stage 積分法 26
第五章 具剪變形之樑的動態反應之數值模擬 28
第六章 數值計算例 35
6.1不具彈性基座之等斷面懸臂樑之動態反應 35
6.2具彈性基座之兩段不等斷面懸臂樑之動態反應37
第七章 結論 39
參考文獻 40
附錄一 剪力修正係數 A
附錄二 五個離散點的權重係數一覽表 B
附錄三 六個離散點的權重係數一覽表 C
附錄四 七個離散點的權重係數一覽表 D
附錄五 八個離散點的權重係數一覽表 E
附錄六 九個離散點的權重係數一覽表 F
自述 G

參考文獻
【1】R.E. Bellman and J. Casti “Differential Quadrature and Long-term Integration”,Journal of Mathematical Analysis and Applications,34, 235-238, 1971.
【2】F. Civan and C. M. Sliepcevich “Differential Quadratural to Transport Processes”, J. Math. Anal. Appl. ,93 , 206-221,1983.
【3】S.K. Jang , C.W. Bert and A.G. Striz “Application of Differential Quadrature to Static Analysis of Structural Components”, Int. J. Numer. Methods eng. ,28, 561-577,1989.
【4】J.O. Mingle, “ The Method of Differential Quadrature for Transient Nonlinear Diffusion ”,J. Math. Anal.,60,569-599,1977.
【5】F. Civan and C. M. Sliepcevich “Differential Quadratural for Multi-dimentional Problems”, J. Math. Anal. Appl. 101, 423-443, 1984.
【6】Chen CN. “A Differential Quadrature Element Method”, Proc. 1stInternational Conference on Computational Engineering and Computer Simulation,Changsha, China, 25-34,1995.
【7】Chen CN. “Generalization of Differential Quadrature Discretization" ,Numerical Algorithms,Vol.22,167-182,1999.
【8】Chen CN. “A Generalized Differential Quadrature Element Method”, Computer Methods in Applied Mechanics and Engineering,Vol.188, 553-556,2000.
【9】Chen CN. “Analysis of 3-D Frame Problems by DQEM Using EDQ”, Advances in Engineering Software 2000, accepted for publication.
【10】Chen CN. “Differential Quadrature Element Analysis Using Extended Differential Quadrature”, Computer& Mathematics with Appl. ,Vol. 39,65-79,1999.
【11】Chen CN. “ The Warping Torsion Bar Model of the Differential Quadrature Element Method”,Computer & Structures,Vol.66,249-257,1998.
【12】Chen CN. “ A Differential Quadrature Finite Element Method”,Applied Mechanics in the Americas (eds D. Pamplona et al.) , American Academy of Mechanics,Vol.6,309-312,1998.
【13】Chen CN. “The Two-dimensional Frame Model of the Differential Quadrarure Element Method”, Computers & Structures.
【14】林育男 “數值積分示微分元素法的研究”,國立成功大學造船船舶機械工程研究所碩士論文,1995.
【15】宋治勇 “數值積分示微分元素法振動分析模式”,國立成功大學造船暨船舶機械工程研究所碩士論文,1996.
【16】黃志偉 “數值積分示微分元素法剪變形變斷面樑分析模式”,國立成功大學造船暨船舶機械工程研究所碩士論文,1997.
【17】謝明錡 “數值積分示微分元素法具彈性基座樑分析模式”,國立成功大學造船暨船舶機械工程研究所碩士論文,1997.
【18】李盈賢 “應用DQEM分析彈性基座之變斷面剪變形樑” ,國立成功大學造船暨船舶機械工程研究所碩士論文,2001.
【19】G. R. Cowper , “ The Shear Coefficient in Timoshenko’s Beam ”, Journal of Applied Mechanics , 335-340, June,1966.
【20】Oktay Ural “有限元素元素法導論” 科技圖書股份有限公司.
【21】J.B.Carr, “The Effect of Shear Flexibility and Rotatory Inertia on the Natural Frequencies of Uniform Beams”, The Aeronatutical Quarterly,Vol.21,79-90,1970.
【22】Chang Shu and Bryan E. Richard “Application of Generalized Differential Quadrature to solve Two-Dimensional Incompressible Navier-Stokes Equations”, International Journal For Numerical Method in Fluids,Vol. 15,791-798,1992.