Engineering Analysis with ANSYS Software Book

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