Engineering Analysis with ANSYS Software (eBook)

ENGINEERING ANALYSIS WITH ANSYS SOFTWARE 4
COPYRIGHT PAGE 5
CONTENTS 6
PREFACE 14
THE AIMS AND SCOPE OF THE BOOK 16
CHAPTER 1 BASICS OF FINITE-ELEMENT METHOD 18
1.1 METHOD OF WEIGHTED RESIDUALS 19
1.1.1 Sub-domain method (Finite volume method) 19
1.1.2 Galerkin method 21
1.2 RAYLEIGH–RITZ METHOD 22
1.3 FINITE-ELEMENT METHOD 24
1.3.1 One-element case 27
1.3.2 Three-element case 28
1.4 FEM IN TWO-DIMENSIONAL ELASTOSTATIC PROBLEMS 31
1.4.1 Elements of finite-element procedures in the analysis of plane elastostatic problems 32
1.4.2 Fundamental formulae in plane elastostatic problems 33
1.4.2.1 Equations of equilibrium 33
1.4.2.2 Strain–displacement relations 33
1.4.2.3 Stress–strain relations (constitutive equations) 34
1.4.2.4 Boundary conditions 36
1.4.3 Variational formulae in elastostatic problems: the principle of virtual work 38
1.4.4 Formulation of the fundamental finite-element equations in plane elastostatic problems 38
1.4.4.1 Strain–displacement matrix or [B] matrix 38
1.4.4.2 Stress–strain matrix or [D] matrix 42
1.4.4.3 Element stiffness equations 42
1.4.4.4 Global stiffness equations 44
1.4.4.5 Example: Finite-element calculations for a square plate subjected to uniaxial uniform tension 47
BIBLIOGRAPHY 51
CHAPTER 2 OVERVIEW OF ANSYS STRUCTURE AND VISUAL CAPABILITIES 54
2.1 INTRODUCTION 54
2.2 STARTING THE PROGRAM 55
2.2.1 Preliminaries 55
2.2.2 Saving and restoring jobs 57
2.2.3 Organization of files 58
2.2.4 Printing and plotting 59
2.2.5 Exiting the program 60
2.3 PREPROCESSING STAGE 60
2.3.1 Building a model 60
2.3.1.1 Defining element types and real constants 61
2.3.1.2 Defining material properties 63
2.3.2 Construction of the model 64
2.3.2.1 Creating the model geometry 64
2.3.2.2 Applying loads 65
2.4 SOLUTION STAGE 66
2.5 POSTPROCESSING STAGE 67
CHAPTER 3 APPLICATION OF ANSYS TO STRESS ANALYSIS 68
3.1 CANTILEVER BEAM 68
3.1.1 Example problem: A cantilever beam 69
3.1.2 Problem description 70
3.1.2.1 Review of the solutions obtained by the elementary beam theory 70
3.1.3 Analytical procedures 70
3.1.3.1 Creation of an analytical model 70
3.1.3.2 Input of the elastic properties of the beam material 73
3.1.3.3 Finite-element discretization of the beam area 74
3.1.3.4 Input of boundary conditions 79
3.1.3.5 Solution procedures 88
3.1.3.6 Graphical representation of the results 90
3.1.4 Comparison of FEM results with experimental ones 93
3.1.5 Problems to solve 93
APPENDIX: PROCEDURES FOR CREATING STEPPED BEAMS 97
A3.1 Creation of a stepped beam 97
A3.1.1 How to cancel the selection of areas 98
A3.2 Creation of a stepped beam with a rounded fillet 98
A3.2.1 How to display area numbers 101
3.2 THE PRINCIPLE OF ST. VENANT 101
3.2.1 Example problem: An elastic strip subjected to distributed uniaxial tensile stress or negative pressure at one end and clamped at the other end 101
3.2.2 Problem description 102
3.2.3 Analytical procedures 102
3.2.3.1 Creation of an analytical model 102
3.2.3.2 Input of the elastic properties of the strip material 103
3.2.3.3 Finite-element discretization of the strip area 103
3.2.3.4 Input of boundary conditions 105
3.2.3.5 Solution procedures 106
3.2.3.6 Contour plot of stress 109
3.2.4 Discussion 109
3.3 STRESS CONCENTRATION DUE TO ELLIPTIC HOLES 110
3.3.1 Example problem: An elastic plate with an elliptic hole in its center subjected to uniform longitudinal tensile stress & #963
3.3.2 Problem description 111
3.3.3 Analytical procedures 111
3.3.3.1 Creation of an analytical model 111
3.3.3.2 Input of the elastic properties of the plate material 114
3.3.3.3 Finite-element discretization of the quarter plate area 115
3.3.3.4 Input of boundary conditions 116
3.3.3.5 Solution procedures 117
3.3.3.6 Contour plot of stress 118
3.3.3.7 Observation of the variation of the longitudinal stress distribution in the ligament region 118
3.3.4 Discussion 119
3.3.5 Problems to solve 122
3.4 STRESS SINGULARITY PROBLEM 123
3.4.1 Example problem: An elastic plate with a crack of length 2a in its center subjected to uniform longitudinal tensile stress & #963
3.4.2 Problem description 123
3.4.3 Analytical procedures 124
3.4.3.1 Creation of an analytical model 124
3.4.3.2 Input of the elastic properties of the plate material 127
3.4.3.3 Finite-element discretization of the centercracked tension plate area 127
3.4.3.4 Input of boundary conditions 130
3.4.3.5 Solution procedures 131
3.4.3.6 Contour plot of stress 132
3.4.4 Discussion 133
3.4.5 Problems to solve 135
3.5 TWO-DIMENSIONAL CONTACT STRESS 137
3.5.1 Example problem: An elastic cylinder with a radius of length(a) pressed against a flat surface of a linearly elastic medium by a forcé 137
3.5.2 Problem description 137
3.5.3 Analytical procedures 138
3.5.3.1 Creation of an analytical model 138
3.5.3.2 Input of the elastic properties of the material for the cylinder and the flat plate 140
3.5.3.3 Finite-element discretization of the cylinder and the flat plate areas 140
3.5.3.4 Input of boundary conditions 150
3.5.3.5 Solution procedures 152
3.5.3.6 Contour plot of stress 153
3.5.4 Discussion 153
3.5.5 Problems to solve 155
REFERENCES 158
CHAPTER 4 MODE ANALYSIS 160
4.1 INTRODUCTION 160
4.2 MODE ANALYSIS OF A STRAIGHT BAR 161
4.2.1 Problem description 161
4.2.2 Analytical solution 161
4.2.3 Model for finite-element analysis 162
4.2.3.1 Element type selection 162
4.2.3.2 Real constants for beam element 164
4.2.3.3 Material properties 164
4.2.3.4 Create keypoints 166
4.2.3.5 Create a line for beam element 168
4.2.3.6 Create mesh in a line 169
4.2.3.7 Boundary conditions 171
4.2.4 Execution of the analysis 174
4.2.4.1 Definition of the type of analysis 174
4.2.4.2 Execute calculation 176
4.2.5 Postprocessing 178
4.2.5.1 Read the calculated results of the first mode of vibration 178
4.2.5.2 Plot the calculated results 178
4.2.5.3 Read the calculated results of the second and third modes of vibration 178
4.3 MODE ANALYSIS OF A SUSPENSION FOR HARD-DISC DRIVE 180
4.3.1 Problem description 180
4.3.2 Create a model for analysis 180
4.3.2.1 Element type selection 180
4.3.2.2 Real constants for beam element 182
4.3.2.3 Material properties 185
4.3.2.4 Create keypoints 185
4.3.2.5 Create areas for suspension 188
4.3.2.6 Boolean operation 192
4.3.2.7 Create mesh in areas 194
4.3.2.8 Boundary conditions 196
4.3.3 Analysis 199
4.3.3.1 Define the type of analysis 199
4.3.3.2 Execute calculation 199
4.3.4 Postprocessing 200
4.3.4.1 Read the calculated results of the first mode of vibration 200
4.3.4.2 Plot the calculated results 200
4.3.4.3 Read the calculated results of higher modes of vibration 201
4.4 MODE ANALYSIS OF A ONE-AXIS PRECISION MOVING TABLE USING ELASTIC HINGES 205
4.4.1 Problem description 205
4.4.2 Create a model for analysis 206
4.4.2.1 Select element type 206
4.4.2.2 Material properties 206
4.4.2.3 Create keypoints 209
4.4.2.4 Create areas for the table 210
4.4.2.5 Create mesh in areas 214
4.4.2.6 Boundary conditions 218
4.4.3 Analysis 222
4.4.3.1 Define the type of analysis 222
4.4.3.2 Execute calculation 225
4.4.4 Postprocessing 226
4.4.4.1 Read the calculated results of the first mode of vibration 226
4.4.4.2 Plot the calculated results 226
4.4.4.3 Read the calculated results of the second and third modes of vibration 227
4.4.4.4 Animate the vibration mode shape 228
CHAPTER 5 ANALYSIS FOR FLUID DYNAMICS 232
5.1 INTRODUCTION 232
5.2 ANALYSIS OF FLOW STRUCTURE IN A DIFFUSER 233
5.2.1 Problem description 233
5.2.2 Create a model for analysis 233
5.2.2.1 Select kind of analysis 233
5.2.2.2 Element type selection 234
5.2.2.3 Create keypoints 236
5.2.2.4 Create areas for diffuser 238
5.2.2.5 Create mesh in lines and areas 239
5.2.2.6 Boundary conditions 243
5.2.3 Execution of the analysis 248
5.2.3.1 FLOTRAN set up 248
5.2.4 Execute calculation 250
5.2.5 Postprocessing 251
5.2.5.1 Read the calculated results of the first mode of vibration 251
5.2.5.2 Plot the calculated results 251
5.2.5.3 Plot the calculated results by path operation 254
5.3 ANALYSIS OF FLOW STRUCTURE IN A CHANNEL WITH A BUTTERFLY VALVE 259
5.3.1 Problem description 259
5.3.2 Create a model for analysis 259
5.3.2.1 Select kind of analysis 259
5.3.2.2 Select element type 260
5.3.2.3 Create keypoints 260
5.3.2.4 Create areas for flow channel 262
5.3.2.5 Subtract the valve area from the channel area 262
5.3.2.6 Create mesh in lines and areas 263
5.3.2.7 Boundary conditions 265
5.3.3 Execution of the analysis 268
5.3.3.1 FLOTRAN set up 268
5.3.4 Execute calculation 270
5.3.5 Postprocessing 271
5.3.5.1 Read the calculated results 271
5.3.5.2 Plot the calculated results 272
5.3.5.3 Detailed view of the calculated flow velocity 273
5.3.5.4 Plot the calculated results by path operation 276
CHAPTER 6 APPLICATION OF ANSYS TO THERMO MECHANICS 280
6.1 GENERAL CHARACTERISTIC OF HEAT TRANSFER PROBLEMS 280
6.2 HEAT TRANSFER THROUGH TWO WALLS 282
6.2.1 Problem description 282
6.2.2 Construction of the model 282
6.2.3 Solution 293
6.2.4 Postprocessing 297
6.3 STEADY-STATE THERMAL ANALYSIS OF A PIPE INTERSECTION 302
6.3.1 Description of the problem 302
6.3.2 Preparation for model building 305
6.3.3 Construction of the model 308
6.3.4 Solution 315
6.3.5 Postprocessing stage 323
6.4 HEAT DISSIPATION THROUGH RIBBED SURFACE 329
6.4.1 Problem description 329
6.4.2 Construction of the model 330
6.4.3 Solution 338
6.4.4 Postprocessing 342
CHAPTER 7 APPLICATION OF ANSYS TO CONTACT BETWEEN MACHINE ELEMENTS 348
7.1 GENERAL CHARACTERISTICS OF CONTACT PROBLEMS 348
7.2 EXAMPLE PROBLEMS 349
7.2.1 Pin-in-hole interference fit 349
7.2.1.1 Problem description 349
7.2.1.2 Construction of the model 350
7.2.1.3 Material properties and element type 355
7.2.1.4 Meshing 356
7.2.1.5 Creation of contact pair 359
7.2.1.6 Solution 364
7.2.1.7 Postprocessing 369
7.2.2 Concave contact between cylinder and two blocks 376
7.2.2.1 Problem description 376
7.2.2.2 Model construction 377
7.2.2.3 Material properties 382
7.2.2.4 Meshing 385
7.2.2.5 Creation of contact pair 389
7.2.2.6 Solution 391
7.2.2.7 Postprocessing 396
7.2.3 Wheel-on-rail line contact 399
7.2.3.1 Problem description 399
7.2.3.2 Model construction 402
7.2.3.3 Properties of material 408
7.2.3.4 Meshing 409
7.2.3.5 Creation of contact pair 415
7.2.3.6 Solution 418
7.2.3.7 Postprocessing 421
7.2.4 O-ring assembly 427
7.2.4.1 Problem description 427
7.2.4.2 Model construction 429
7.2.4.3 Selection of materials 430
7.2.4.4 Geometry of the assembly and meshing 440
7.2.4.5 Creating contact interface 444
7.2.4.6 Solution 453
7.2.4.7 Postprocessing (first load step) 459
7.2.4.8 Solution (second load step) 461
7.2.4.9 Postprocessing (second load step) 468
INDEX 470
A 470
B 470
C 470
D 470
E 471
F 471
G 471
H 471
I 471
J 471
K 471
L 471
M 472
N 472
O 472
P 472
R 472
S 472
T 473
U 473
V 473
W 473
X 473
Y 473
Equations of equilibrium 33
Problem description 349
Problem description 427