Engineering Analysis with ANSYS Software > 유한요소법

Preface xiii
The Aims and Scope of the Book xv
Basics of finite-element method 1
Method of Weighted Residuals 2
Sub-domain method (Finite volume method) 2
Galerkin method 4
Rayleigh-Ritz Method 5
Finite-Element Method 7
One-element case 10
Three-element case 11
FEM in Two-Dimensional Elastostatic Problems 14
Elements of finite-element procedures in the analysis of plane elastostatic problems 15
Fundamental formulae in plane elastostatic problems 16
Equations of equilibrium 16
Strain-displacement relations 16
Stress-strain relations (constitutive equations) 17
Boundary conditions 19
Variational formulae in elastostatic problems: the principle of virtual work 21
Formulation of the fundamental finite-element equations in plane elastostatic problems 21
Strain-displacement matrix or [B] matrix 21
Stress-strain matrix or [D] matrix 25
Element stiffness equations 25
Global stiffness equations 27
Example: Finite-element calculations for a square plate subjected to uniaxialuniform tension 30
Bibliography 34
Overview of ANSYS structure and visual Capabilities 37
Introduction 37
Starting the Program 38
Preliminaries 38
Saving and restoring jobs 40
Organization of files 41
Printing and plotting 42
Exiting the program 43
Preprocessing Stage 43
Building a model 43
Defining element types and real constants 44
Defining material properties 46
Construction of the model 47
Creating the model geometry 47
Applying loads 48
Solution Stage 49
Postprocessing Stage 50
Application of ANSYS to Stress Analysis 51
Cantilever beam 51
Example problem: A cantilever beam 52
Problem description 53
Review of the solutions obtained by the elementary beam theory 53
Analytical procedures 53
Creation of an analytical model 53
Input of the elastic properties of the beam material 56
Finite-element discretization of the beam area 57
Input of boundary conditions 62
Solution procedures 71
Graphical representation of the results 73
Comparison of FEM results with experimental ones 76
Problems to solve 76
Procedures for Creating Stepped Beams 80
Creation of a stepped beam 80
How to cancel the selection of areas 81
Creation of a stepped beam with a rounded fillet 81
How to display area numbers 84
The Principle of St. Venant 84
Example problem: An elastic strip subjected to distributed uniaxial tensile stress or negative pressure at one end and clamped at the other end 84
Problem description 85
Analytical procedures 85
Creation of an analytical model 85
Input of the elastic properties of the strip material 86
Finite-element discretization of the strip area 86
Input of boundary conditions 88
Solution procedures 89
Contour plot of stress 92
Discussion 92
Stress Concentration Due to Elliptic Holes 93
Example problem: An elastic plate with an elliptic hole in its center subjected to uniform longitudinal tensile stress [sigma][subscript o] at one end and damped at the other end 93
Problem description 94
Analytical procedures 94
Creation of an analytical model 94
Input of the elastic properties of the plate material 97
Finite-element discretization of the quarter plate area 98
Input of boundary conditions 99
Solution procedures 100
Contour plot of stress 101
Observation of the variation of the longitudinal stress distribution in the ligament region 101
Discussion 102
Problems to solve 105
Stress Singularity Problem 106
Example problem: An elastic plate with a crack of length 2a in its center subjected to uniform longitudinal tensile stress [sigma][subscript 0] at one end and clamped at the other end 106
Problem description 106
Analytical procedures 107
Creation of an analytical model 107
Input of the elastic properties of the plate material 110
Finite-element discretization of the centercracked tension plate area 110
Input of boundary conditions 113
Solution procedures 114
Contour plot of stress 115
Discussion 116
Problems to solve 118
Two-Dimensional Contact Stress 120
Example problem: An elastic cylinder with a radius of length (a) pressed against a flat surface of a linearly elastic medium by a force 120
Problem description 120
Analytical procedures 121
Creation of an analytical model 121
Input of the elastic properties of the material for the cylinder and the flat plate 123
Finite-element discretization of the cylinder and the flat plate areas 123
Input of boundary conditions 133
Solution procedures 135
Contour plot of stress 135
Discussion 136
Problems to solve 138
References 141
Mode Analysis 143
Introduction 143
Mode Analysis of A Straight Bar 144
Problem description 144
Analytical solution 144
Model for finite-element analysis 145
Element type selection 145
Real constants for beam element 147
Material properties 147
Create keypoints 149
Create a line for beam element 151
Create mesh in a line 152
Boundary conditions 154
Execution of the analysis 157
Definition of the type of analysis 157
Execute calculation 159
Postprocessing 161
Read the calculated results of the first mode of vibration 161
Plot the calculated results 161
Read the calculated results of the second and third modes of vibration 161
Mode Analysis of a Suspension for Hard-Disc Drive 163
Problem description 163
Create a model for analysis 163
Element type selection 163
Real constants for beam element 165
Material properties 168
Create keypoints 168
Create areas for suspension 171
Boolean operation 175
Create mesh in areas 177
Boundary conditions 179
Analysis 182
Define the type of analysis 182
Execute calculation 182
Postprocessing 183
Read the calculated results of the first mode of vibration 183
Plot the calculated results 183
Read the calculated results of higher modes of vibration 184
Mode Analysis of a One-Axis Precision Moving Table Using Elastic Hinges 188
Problem description 188
Create a model for analysis 189
Select element type 189
Material properties 189
Create keypoints 192
Create areas for the table 193
Create mesh in areas 197
Boundary conditions 201
Analysis 205
Define the type of analysis 205
Execute calculation 208
Postprocessing 209
Read the calculated results of the first mode of vibration 209
Plot the calculated results 209
Read the calculated results of the second and third modes of vibration 210
Animate the vibration mode shape 211
Analysis For Fluid Dynamics 215
Introduction 215
Analysis of Flow Structure in A Diffuser 216
Problem description 216
Create a model for analysis 216
Select kind of analysis 216
Element type selection 217
Create keypoints 219
Create areas for diffuser 221
Create mesh in lines and areas 222
Boundary conditions 226
Execution of the analysis 231
Flotran set up 231
Execute calculation 233
Postprocessing 234
Read the calculated results of the first mode of vibration 234
Plot the calculated results 234
Plot the calculated results by path operation 237
Analysis of flow structure in a channel with a butterfly Valve 242
Problem description 242
Create a model for analysis 242
Select kind of analysis 242
Select element type 243
Create keypoints 243
Create areas for flow channel 245
Subtract the valve area from the channel area 245
Create mesh in lines and areas 246
Boundary conditions 248
Execution of the analysis 251
Flotran set up 251
Execute calculation 253
Postprocessing 254
Read the calculated results 254
Plot the calculated results 255
Detailed view of the calculated flow velocity 256
Plot the calculated results by path operation 259
Application of ANSYS to Thermo Mechanics 263
General characteristic of heat transfer problems 263
Heat transfer through two walls 265
Problem description 265
Construction of the model 265
Solution 276
Postprocessing 280
Steady-State Thermal Analysis of a Pipe Intersection 285
Description of the problem 285
Preparation for model building 288
Construction of the model 291
Solution 298
Postprocessing stage 306
Heat Dissipation Through Ribbed Surface 312
Problem description 312
Construction of the model 313
Solution 321
Postprocessing 325
Application of ANSYS to Contact Between Machine Elements 331
General Characteristics of Contact Problems 331
Example Problems 332
Pin-in-hole interference fit 332
Problem description 332
Construction of the model 333
Material properties and element type 338
Meshing 339
Creation of contact pair 342
Solution 347
Postprocessing 352
Concave contact between cylinder and two blocks 359
Problem description 359
Model construction 360
Material properties 365
Meshing 368
Creation of contact pair 372
Solution 374
Postprocessing 379
Wheel-on-rail line contact 382
Problem description 382
Model construction 385
Properties of material 391
Meshing 392
Creation of contact pair 398
Solution 401
Postprocessing 404
0-ring assembly 410
Problem description 410
Model construction 412
Selection of materials 413
Geometry of the assembly and meshing 423
Creating contact interface 427
Solution 436
Postprocessing (first load step) 442
Solution (second load step) 444
Postprocessing (second load step) 451
Index 453