كتاب The Finite Element Method and Applications in Engineering Using ANSYS

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The Finite Element Method and Applications in Engineering Using ANSYS
by
Erdogan Madenci
Ibrahim Guven
The University of Arizona

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TABLE OF CONTENTS
PREFACE V
LIST OF PROBLEMS SOLVED xiii
1 INTRODUCTION 1
LI Concept 1
1.2 Nodes 3
1.3 Elements 4
1.4 Direct Approach 5
1.4.1 Linear Spring 5
1.4.2 Heat Flow 6
1.4.3 Assembly of the Global System of Equations 8
1.4.4 Solution of the Global System of Equations 12
1.4.5 Boundary Conditions 13
2 FUNDAMENTALS OF ANSYS 15
2.1 Useful Definitions 15
2.2 Before an ANSYS Session 16
2.2.1 Analysis Discipline 16
2.2.2 Time Dependence 18
2.2.3 Nonlinearity 18
2.2.4 Practical Modeling Considerations 19
2.3 Organization of ANSYS Software 25
2.4 ANSYS Analysis Approach 26
2.4.1 ANSYS Preprocessor 27
2.4.2 ANSYS Solution Processor 27
2.4.3 ANSYS General Postprocessor 27
2.4.4 ANSYS Time History Postprocessor 27
2.5 ANSYS File Structure 27
2.5.1 Database File 28
2.5.2 Log File 28
2.5.3 ErrorFile 28
2.5.4 Results Files 28viii FEM WITH ANSYS^
2.6 Description of ANSYS Menus and Windows 29
2.6.1 Utility Menu 30
2.6.2 Main Menu 31
2.6.3 Toolbar 32
2.6.4 Input Field 32
2.6.5 Graphics Window 32
2.6.6 Output Window 32
2.7 Using the ANSYS Help System 32
2.7.1 Help Contents 33
2.7.2 Help Index 33
2.7.3 Search in Help 33
2.7.4 Verification Manual 35
3 FUNDAMENTALS OF DISCRETIZATION 37
3.1 Local and Global Numbering 37
3.2 Approximation Functions 37
3.3 Coordinate Systems 43
3.3.1 Generalized Coordinates 43
3.3.2 Global Coordinates 43
3.3.3 Local Coordinates 43
3.3.4 Natural Coordinates 43
3.4 Shape Functions 51
3.4.1 Linear Line Element with Two Nodes 54
3.4.2 Quadratic Line Element with Three Nodes:
Centroidal Coordinate 56
3.4.3 Linear Triangular Element with Three Nodes:
Global Coordinate 58
3.4.4 Quadratic Triangular Element with Six Nodes 59
3.4.5 Linear Quadrilateral Element with Four Nodes:
Centroidal Coordinate 62
3.5 Isoparametric Elements: Curved Boundaries 64
3.6 Numerical Evaluation of Integrals 68
3.6.1 Line Integrals 68
3.6.2 Triangular Area Integrals 72
3.6.3 Quadrilateral Area Integrals 75
3.7 Problems 78
4 ANSYS PREPROCESSOR 83
4.1 Fundamentals of Modeling 83
4.2 Modeling Operations 83
4.2.1 Title 84TABLE OF CONTENTS ix
4.2.2 Elements 85
4.2.3 Real Constants 89
4.2.4 Material Properties 92
4.2.5 Element Attributes 96
4.2.6 Interaction with the Graphics Window:
Picking Entities 96
4.2.7 Coordinate Systems 99
4.2.8 Working Plane 102
4.3 Solid Modeling 105
4.3.1 Bottom-up Approach: Entities 106
4.3.2 Top-down Approach: Primitives 112
4.4 Boolean Operators 118
4.4.1 Adding 118
4.4.2 Subtracting 120
4.4.3 Overlap 120
4.4.4 Gluing 121
4.4.5 Dividing 121
4.5 Additional Operations 124
4.5.1 Extrusion and Sweeping 124
4.5.2 Moving and Copying 128
4.5.3 Keeping/Deleting Original Entities 128
4.5.4 Listing Entities 130
4.5.5 Deleting Entities 130
4.6 Viewing a Model 131
4.6.1 Plotting: Pan, Zoom, and Rotate Functions 131
4.6.2 Plotting/Listing Entities 134
4.6.3 Numbers in the Graphics Window 134
4.7 Meshing 134
4.7.1 Automatic Meshing 135
4.7.2 Manipulation of the Mesh 141
4.8 Selecting and Components 144
4.8.1 Selecting Operations 144
4.8.2 Components 148
5 ANSYS SOLUTION AND POSTPROCESSING 149
5.1 Overview 149
5.2 Solution 150
5.2.1 Analysis Options/Solution Controls 150
5.2.2 Boundary Conditions 153
5.2.3 Initial Conditions 154
5.2.4 Body Loads 154X FEM WITH ANSYS
5.2.5 Solution in Single and Multiple Load Steps 154
5.2.6 Failure to Obtain Solution 158
5.3 Postprocessing 160
5.3.1 General Postprocessor 160
5.3.2 Time History Postprocessor 160
5.3.3 Read Results 161
5.3.4 Plot Results , 163
5.3.5 Element Tables 167
5.3.6 List Results 170
5.4 Example: One-dimensional Transient Heat Transfer 170
6 FINITE ELEMENT EQUATIONS 187
6.1 Method of Weighted Residuals 187
6.1.1 Example: One-dimensional Differential Equation
with Line Elements 189
6.1.2 Example: Two-dimensional Differential Equation
with Linear Triangular Elements 197
6.1.3 Example: Two-dimensional Differential Equation
with Linear Quadrilateral Elements 216
6.2 Principle of Minimum Potential Energy 235
6.2.1 Example: One-dimensional Analysis with
Line Elements 242
6.2.2 Two-dimensional Structural Analysis 248
6.3 Problems 289
7 USE OF COMMANDS IN ANSYS 297
7.1 Basic ANSYS Commands 297
7.1.1 Operators and Functions 298
7.1.2 Defining Parameters 304
7.2 A Typical Input File 307
7.3 Selecting Operations 309
7.4 Extracting Information from ANSYS 314
7.5 Programming with ANSYS 317
7.5.1 DO Loops 317
7.5.2 IF Statements 318
7.5.3 /OUTPUT and *VWRITE Commands 321
7.6 Macro Files 322
7.7 Useful Resources 324
7.7.1 Using the Log File for Programming 325
7.7.2 Using the Verification Problems for Programming 326TABLE OF CONTENTS xi
8 LINEAR STRUCTURAL ANALYSIS 329
8.1 Static Analysis 329
8.L1 Trusses 329
8.1.2 Beams 337
8.1.3 Three-dimensional Problems 342
8.1.4 Two-dimensional Idealizations 346
8.1.5 Plates and Shells 373
8.2 Linear Buckling Analysis 403
8.3 Thermomechanical Analysis 412
8.4 Fracture Mechanics Analysis 421
8.5 Dynamic Analysis 433
8.5.1 Modal Analysis 434
8.5.2 Harmonic Analysis 444
8.5.3 Transient Analysis 459
9 LINEAR ANALYSIS OF FIELD PROBLEMS 477
9.1 Heat Transfer Problems 477
9.1.1 Steady-state Analysis 478
9.1.2 Transient Analysis 520
9.1.3 Radiation Analysis 543
9.2 Moisture Diffusion 549
10 NONLINEAR STRUCTURAL ANALYSIS 565
10.1 Geometric Nonlinearity 569
10.1.1 Large Deformation Analysis of a Plate 570
10.1.2 Post-buckling Analysis of a Plate with a Hole 573
10.2 Material Nonlinearity 578
10.2.1 Plastic Deformation of an Aluminum Sphere 579
10.2.2 Plastic Deformation of an Aluminum Cylinder 583
10.2.3 Stress Analysis of a Reinforced Viscoelastic
Cylinder 589
10.2.4 Viscoplasticity Analysis of a Eutectic Solder
Cylinder 592
10.2.5 Combined Plasticity and Creep 599
10.3 Contact 605
10.3.1 Contact Analysis of a Block Dropping on a Beam 607
10.3.2 Simulation of a Nano-indentation Test 613xii FEM WITH ANSYS
11 ADVANCED TOPICS IN ANSYS 621
11.1 Coupled Degrees of Freedom 621
11.2 Constraint Equations 624
11.3 Submodeling 629
11.4 Substructuring: Superelements 636
11.4.1 Generation Pass 638
11.4.2 Use Pass 644
11.4.3 Expansion Pass 646
11.5 Interacting with External Files 647
11.5.1 Reading an Input File 647
11.5.2 Writing Data to External ASCII Files 648
11.5.3 Executing an External File 652
11.5.4 Modifying ANSYS Results 654
11.6 Modifying the ANSYS GUI 654
11.6.1 GUI Development Demonstration 662
11.6.2 GUI Modification for Obtaining a Random
Load Profile 671
11.6.3 Function Block for Selecting Elements Using
a Pick Menu 675
REFERENCES 679
INDEX 68

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