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The finite element method of lines : theory and applications 🔍
SiYuan著 Science Press, Beijing, ©1993
中文 [zh] · 英语 [en] · PDF · 17.2MB · 1993 · 📗 未知类型的图书 · 🚀/duxiu/upload · Save
描述
THE FINITE ELEMENT METHOD OF LINES Theory and Applications 1
Contents 6
Preface 10
PART I ORDINARY DIFFERENTIAL EQUATIONS 12
Chapter 1 Mathematical Preliminaries 14
1.1 ODEs 14
1.2 BCs 16
1.3 An Illustrative Example 17
Chapter 2 ODE Solver COLSYS 18
2.1 ODE Software 18
2.2 Standard ODE Form 19
2.3 The Method and Features 20
2.4 Use of COLSYS 23
2.5 A Sample Programme 24
2.6 Rules and Tips 29
Chapter 3 ODE Conversion Techniques 32
3.1 Trivial ODE Technique 33
3.2 Interval Mapping Technique 33
3.3 Equivalent ODE Technique 35
3.4 Illustrative Examples 36
3.5 Nonseparated BCs 43
3.6 Continuation 44
3.7 Critical Points 47
Chapter 4 ODE-Solver Method in Applications 50
4.1 Minimum Weight of Beams 50
4.2 Minimum Weight of Pinned Columns 53
4.3 Optimal Buckling Loads of Clamped Columns 62
4.4 An Elastic-Plastic Bar under Complex Loading 76
4.5 Two-Dimensional Crack Singularities 85
4.6 Linear Analysis of Thick/Thin Axisymmetric Shells 93
4.7 Nonlinear Analysis of Axisymmetric Thin Shells 107
4.8 An Eigen-Solver 114
4.9 Vibrations of Tall Buildings 127
4.10 Stability of Tall Buildings 142
PART Ⅱ THE METHOD OF LINES(MOL) 148
Chapter 5 MOL for Second-Order Equations 150
5.1 The Poisson Equation 150
5.2 MOL for L-Shaped Domain Problem 153
5.3 Free Vibration of Square Membranes 165
5.4 Parametric FD Scheme on Irregular Line Meshes 173
5.5 The Poisson Equation on Irregular Domains 179
Chapter 6 MOL for Fourth-Order Equations 186
6.1 Thin Plate Bending Problem 186
6.2 Elastic Stability of Rectangular Plates 200
6.3 Free Vibration of Rectangular Plates 204
6.4 Parametric FD Scheme for Fourth-Order Derivatives 206
6.5 Thin Plate Bending on Irregular Domains 216
PART Ⅲ THE FINITE ELEMENT METHOD OF LINES(FEMOL) 224
Chapter 7 FEMOL Ⅰ:Fundamentals 226
7.1 Basic Description 226
7.2 Standard Formulation 234
7.3 Degenerate End-Sides 243
7.4 Degenerate Mesh Lines 252
7.5 Other Special Elements 258
7.6 Numerical Results 268
7.7 Remarks and Discussions 284
Chapter 8 FEMOL Ⅱ:Linear Applications 288
8.1 Plane Elasticity 289
8.2 Thin Plate Bending 303
8.3 Mindlin-Reissner Plate Bending 317
8.4 Shallow Shells 330
8.5 Elements in Polar Coordinates 343
Chapter 9 FEMOL Ⅲ:Nonlinear Applications 362
9.1 General Description 363
9.2 Optimal Cross-Section of Torsional Bars 366
9.3 Membrane Contact with a Rigid Foundation 381
9.4 Free Vibration of Membranes 387
9.5 Large Deflection of Membranes 393
9.6 Elastic-Plastic Torsion 406
Bibliography 416
Index 428
备用文件名
upload/chinese_2025_10/sciencereading1/B8F7B5C05E1BA441B9AD44339F69678CE000.pdf
备选作者
TH-OCR 2007
备选作者
Si Yuan
备用版本
China, People's Republic, China
备用版本
August 1995
备用版本
1, 1993-01
元数据中的注释
producers:
TH-OCR 2000 (C++/Win32)
备用描述
THE FINITE ELEMENT METHOD OF LINES Theory and Applications 1
Contents 6
Preface 10
PART I ORDINARY DIFFERENTIAL EQUATIONS 12
Chapter 1 Mathematical Preliminaries 14
1.1 ODEs 14
1.2 BCs 16
1.3 An Illustrative Example 17
Chapter 2 ODE Solver COLSYS 18
2.1 ODE Software 18
2.2 Standard ODE Form 19
2.3 The Method and Features 20
2.4 Use of COLSYS 23
2.5 A Sample Programme 24
2.6 Rules and Tips 29
Chapter 3 ODE Conversion Techniques 32
3.1 Trivial ODE Technique 33
3.2 Interval Mapping Technique 33
3.3 Equivalent ODE Technique 35
3.4 Illustrative Examples 36
3.5 Nonseparated BCs 43
3.6 Continuation 44
3.7 Critical Points 47
Chapter 4 ODE-Solver Method in Applications 50
4.1 Minimum Weight of Beams 50
4.2 Minimum Weight of Pinned Columns 53
4.3 Optimal Buckling Loads of Clamped Columns 62
4.4 An Elastic-Plastic Bar under Complex Loading 76
4.5 Two-Dimensional Crack Singularities 85
4.6 Linear Analysis of Thick/Thin Axisymmetric Shells 93
4.7 Nonlinear Analysis of Axisymmetric Thin Shells 107
4.8 An Eigen-Solver 114
4.9 Vibrations of Tall Buildings 127
4.10 Stability of Tall Buildings 142
PART II THE METHOD OF LINES(MOL) 148
Chapter 5 MOL for Second-Order Equations 150
5.1 The Poisson Equation 150
5.2 MOL for L-Shaped Domain Problem 153
5.3 Free Vibration of Square Membranes 165
5.4 Parametric FD Scheme on Irregular Line Meshes 173
5.5 The Poisson Equation on Irregular Domains 179
Chapter 6 MOL for Fourth-Order Equations 186
6.1 Thin Plate Bending Problem 186
6.2 Elastic Stability of Rectangular Plates 200
6.3 Free Vibration of Rectangular Plates 204
6.4 Parametric FD Scheme for Fourth-Order Derivatives 206
6.5 Thin Plate Bending on Irregular Domains 216
PART III THE FINITE ELEMENT METHOD OF LINES(FEMOL) 224
Chapter 7 FEMOL I:Fundamentals 226
7.1 Basic Description 226
7.2 Standard Formulation 234
7.3 Degenerate End-Sides 243
7.4 Degenerate Mesh Lines 252
7.5 Other Special Elements 258
7.6 Numerical Results 268
7.7 Remarks and Discussions 284
Chapter 8 FEMOL II:Linear Applications 288
8.1 Plane Elasticity 289
8.2 Thin Plate Bending 303
8.3 Mindlin-Reissner Plate Bending 317
8.4 Shallow Shells 330
8.5 Elements in Polar Coordinates 343
Chapter 9 FEMOL III:Nonlinear Applications 362
9.1 General Description 363
9.2 Optimal Cross-Section of Torsional Bars 366
9.3 Membrane Contact with a Rigid Foundation 381
9.4 Free Vibration of Membranes 387
9.5 Large Deflection of Membranes 393
9.6 Elastic-Plastic Torsion 406
Bibliography 416
Index 428
开源日期
2025-10-27
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