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研究生:鄧忠厚
研究生(外文):TRUNG-HAU DANG
論文名稱:開發一種基於Chebyshev多項式的有限元方法並能用於分析板、殼與流體間的問題
論文名稱(外文):Develop a Finite Element Method Based on Chebyshev Polynomials for the Analysis of Plate, Shell and Fluid Problems
指導教授:黃錦煌博士劉育成博士
指導教授(外文):Prof. Jin-Huang Huang
口試委員:馬劍清劉育成黃錦煌
口試日期:2017-06-26
學位類別:碩士
校院名稱:逢甲大學
系所名稱:機械與電腦輔助工程學系
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:2017
畢業學年度:105
語文別:英文
論文頁數:82
中文關鍵詞:Chebyshev 多項式的有限元方法
外文關鍵詞:Chebyshev finite element
相關次數:
  • 被引用被引用:0
  • 點閱點閱:87
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  • 下載下載:1
  • 收藏至我的研究室書目清單書目收藏:0
This thesis presented a finite element method based on Chebyshev polynomials (CFE) for the analysis of plates, shell and fluid problems. Chebyshev polynomials are sequence of orthogonal polynomials that are defined recursively. The values of the polynomials belong to the interval [-1,1] and vanish at the Gauss points. Therefore, high-order shape functions satisfied the interpolation condition at the points, can be performed with Chebyshev polynomials. The full gauss quadrature rule was used for approximation of integral calculations.
For plate problems, static and free vibration analyses of thick and thin square, rhombic and circular plates, modeled by Reissner-Mindlin plate theory, subjected to different boundary conditions were carried out. Both regular and irregular meshes were considered. Analysis results show that the CFE automatically overcomes shear locking without the formation of spurious zero energy modes by increasing the order of the shape functions.
For shell problems, static and free vibration analyses of cylindrical and spherical shells based on flat shell theory were considered. The obtained results show that CFE can overcome membrane locking that arises in curved structures.
For fluid problems, the CFE was applied to solve the nonhomogeneous wave equation expressed in acoustic pressure. The obtained results showed the CFE is a robust and efficient method.
Acknowledgements i
Abstract ii
Contents iii
List of Figures v
List of Tables vii
Nomenclature ix
List of Acronyms x
Chapter 1: Introduction 1
1.1 Plate bending theory 1
1.2 Shell theory 3
1.3 Fluid mechanics 4
1.4 Finite element method 5
1.5 Shear locking, hourglass and membrane locking phenomena 6
1.6 Novel methods to overcome the phenomena 7
1.7 A finite element method based on Chebyshev polynomials 8
Chapter 2: Introduction to mechanics for structures and fluid 10
2.1 Solid mechanics 10
2.2.1 Plane stress problem 13
2.2.2 Plate problem 14
2.2.3 Shell problems 15
2.2 Fluid mechanics 17
2.3 Coupling of fluid-structure 19
Chapter 3: The construction of a finite element method based on Chebyshev polynomials 21
3.1 Chebyshev polynomials 21
3.2 Lagrangian approximation based on Chebyshev polynomials 24
3.3 Construction shape functions based on Chebyshev polynomials 25
3.4 Apply CFE for structural and compressible fluid analyses 27
3.4.1 Finite element formulation for the plane stress using CFE 27
3.4.2 Finite element formulation for the plate using CFE 28
3.4.3 Finite element formulation for the shell using CFE 30
3.4.4 Finite element formulation for the fluid dynamic using CFE 33
3.4.5 Finite element formulation for coupling of fluid-structure using CFE 33
Chapter 4: Numerical results 35
4.1 Plate analyses 35
4.1.1 Static analysis of plates 35
4.1.2 Free vibration 45
4.2 Shell analyses 52
4.2.1 Cylindrical shell 53
4.2.2 Spherical shell 56
4.3 Fluid-structure coupling 59
Chapter 5. Conclusion 63
5.1. Conclusion 63
5.2. Limitations and future works 63
References 64
Biography 69

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