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研究生:邱乾艷
研究生(外文):Chien-Yen Chiu
論文名稱:三維殼元素於有限元素法之架構
論文名稱(外文):Architecture of An Four Node Degenerated Shell Element in Finite Element Analysis
指導教授:朱聖浩
指導教授(外文):Shan-Haw Ju
學位類別:碩士
校院名稱:國立成功大學
系所名稱:土木工程學系碩博士班
學門:工程學門
學類:土木工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:91
中文關鍵詞:幾何非線性座標轉換矩陣AN 程式有限元素法閉鎖假設應變法材料非線性殼元素
外文關鍵詞:assumed natural straindegenerated shell elementfinite element methodtransformation matrix.geometric nonlinearmaterial nonlinearlockingAN program
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AN程式中一直缺少能準確分析剪力牆及殼結構之殼元素,本文擬採用既有的有限殼元素理論擇優利用,並將新殼元素開發取代原本AN程式中之殼元素。首先使用假設應變法(ASSUMEND STRAIN METHOD)解決閉鎖(LOCKING)之問題,所有應變皆在自然座標(NATURAL COORDINATE SYSTEM)下假設完成,假設橫向剪應變(ASSUMED TRANSVERSE SHEAR STRAIN)為避免剪力閉鎖(SHEAR LOCKING),假設膜應變(ASSUMED MEMBRANE STRAIN)為減輕膜閉鎖(MEMBRANE LOCKING)並可提升膜彎曲(MEMBRANE BENDING)的精度,彎曲應變中考慮厚度方向之高階項,可更準確分析具有厚度之殼結構。此外考慮大變形,使用牛頓拉普生法解非線性問題,並配合FLOW THOERY作為彈塑性分析,以及採用VON MISES CRIERION作為破壞準則。從測試結果確實可看出此殼元素適用之多樣性,及其合理收斂、準確性,這將激勵往後做更真實的剪力牆分析模式。
In AN program (National Cheng-Kung University for a project from the National Science Council), shell element is a lack of the powerful element to analysis the shear walls, and shell-like structures. This thesis proposes a new four-node shell element with assumed strain method to improve the origin shell element in AN program. All the strains are defined and assumed in the natural coordinate system. The assumed transverse shear strains are applied to avoid the shear locking issue. The assumed membrane strains are used to alleviate the membrane locking problem and improve the membrane bending performance. The bending strains and the transverse shear strains contain high order terms of , and it will be more perfect to apply to a wide range of shell problems, i.e. thin, thick, and laminated composite shells. Moreover, for geometric nonlinear analysis, the nonlinear equilibrium equations are solved by Newton-Raphson method, the flow theory is used for elastic-plastic problem and the von Mises criterion is the failure principle. Several examples in this thesis demonstrate that, the versatility to apply and the reasonable accuracy. It will encourage one to find out the more actual model to inquiry shear walls.
摘要 I
ABSTRACT Ⅱ
誌謝 III
CONTENTS IV
LIST OF TABLES Ⅶ
LIST OF FIGURES Ⅷ
NOTATIONS X

CHAPTER 1. INTRODUCTION 1
1.1 Background and purpose 1
1.2 Brief account of the research 2
1.3 Literature review 4
1.4 Illustrate of the finite element program 5

CHAPTER 2. THEORY OF SHELL FINITE ELEMENTS 10
2.1 Formulation of degenerated shell elements 10
2.1.1 Main assumptions 10
2.1.2 Coordinate systems 10
2.1.3 Element geometry 13
2.1.4 Kinematics description 14
2.1.5 Definition of strains 15
2.1.6 Definition of stresses 16
2.1.7 Stiffness evaluation 17
2.2 A new four-node degenerated shell element with assumed natural strain formulation 18
2.2.1 Definition of natural displacement components 18
2.2.2 Definition of natural strain components 19
2.2.3 Structure of natural strains in three-dimension 21
2.2.4 Determination of assumed natural strain field 24
2.2.5 Substituted strain-displacement matrix 25
2.2.6 Elasticity matrix 25
2.2.7 Element stiffness matrix 26

CHAPTER 3. COORDINATE TRANSFORMATION 31
3.1 Introduction 31
3.2 Transformation of vector 32
3.3 Transformation of stress, strain, and material properties 33
3.4 Transformation of stiffness matrices 36
3.5 Summary 37

CHAPTER 4. ELASTO-PLASTIC ANALYSIS CONSIDERING GEOMETRIC AND MATERIAL NONLINEARITIES 39
4.1 Introduction 39
4.2 Updated Lagrangian formulations 39
4.3 Elastic-plastic stress-strain relation 41
4.4 Newton-Raphson Method to solve nonlinear equations 43
4.5 Evaluation of internal force vector and Gauss-point stress 45
4.6 Numerical procedures 49

CHAPTER 5. ACCURACY STUDY Of THE SHELL ELEMENT IN STACTIC ANALYSIS 53
5.1 Introduction 53
5.2 Cantilever beam 53
5.3 Distorted meshes cantilever beam 54
5.4 Clamped square plate under uniform pressure 55
5.5 Twisted cantilever beam 55
5.6 Cook’s membrane problem 55
5.7 Roof’s problem under gravity load 56

CHAPTER 6. CONCLUSIONS AND FUTURE WORKS 71
6.1 Conclusions 71
6.2 Future works 72

REFERENCES 73

APPENDIX A. Derivation Of The BL Matrix For All Nodes 75
APPENDIX A. Nonlinear Parts Of The Element Stiffness Matrices Matrix 91
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