Engineering analysis with ANSYS software

For all engineers and students coming to finite element analysis or to ANSYS software for the first time, this powerful hands-on guide develops a detailed and confident understanding of using ANSYS's powerful engineering analysis tools. The best way to learn complex systems is by means of hands-on experience. With an innovative and clear tutorial based approach, this powerful book provides readers with a comprehensive introduction to all of the fundamental areas of engineering analysis they are likely to require either as part of their studies or in getting up to speed fast with the use of ANSYS software in working life. Opening with an introduction to the principles of the finite element method, the book then presents an overview of ANSYS technologies before moving on to cover key applications areas in detail.Key topics covered:Introduction to the finite element methodGetting started with ANSYS softwarestress analysis dynamics of machines fluid dynamics problemsthermo mechanics contact and surface mechanicsexercises, tutorials, worked examples With its detailed step-by-step explanations, extensive worked examples and sample problems, this book will develop the reader's understanding of FEA and their ability to use ANSYS's software tools to solve their own particular analysis problems, not just the ones set in the book.

Author Notes

Tadeusz Stolarski is Professor of Mechanical Engineering, Brunel University, UK
Y. Nakasone and S. Yoshimoto are both Professors in the Department of Mechanical Engineering, Tokyo University of Science

Preface	p. xiii
The Aims and Scope of the Book	p. xv
Chapter 1 Basics of finite-element method	p. 1
1.1 Method of Weighted Residuals	p. 2
1.1.1 Sub-domain method (Finite volume method)	p. 2
1.1.2 Galerkin method	p. 4
1.2 Rayleigh-Ritz Method	p. 5
1.3 Finite-Element Method	p. 7
1.3.1 One-element case	p. 10
1.3.2 Three-element case	p. 11
1.4 FEM in Two-Dimensional Elastostatic Problems	p. 14
1.4.1 Elements of finite-element procedures in the analysis of plane elastostatic problems	p. 15
1.4.2 Fundamental formulae in plane elastostatic problems	p. 16
1.4.2.1 Equations of equilibrium	p. 16
1.4.2.2 Strain-displacement relations	p. 16
1.4.2.3 Stress-strain relations (constitutive equations)	p. 17
1.4.2.4 Boundary conditions	p. 19
1.4.3 Variational formulae in elastostatic problems: the principle of virtual work	p. 21
1.4.4 Formulation of the fundamental finite-element equations in plane elastostatic problems	p. 21
1.4.4.1 Strain-displacement matrix or [B] matrix	p. 21
1.4.4.2 Stress-strain matrix or [D] matrix	p. 25
1.4.4.3 Element stiffness equations	p. 25
1.4.4.4 Global stiffness equations	p. 27
1.4.4.5 Example: Finite-element calculations for a square plate subjected to uniaxial uniform tension	p. 30
Bibliography	p. 34
Chapter 2 Overview of ANSYS structure and visual Capabilities	p. 37
2.1 Introduction	p. 37
2.2 Starting the Program	p. 38
2.2.1 Preliminaries	p. 38
2.2.2 Saving and restoring jobs	p. 40
2.2.3 Organization of files	p. 41
2.2.4 Printing and plotting	p. 42
2.2.5 Exiting the program	p. 43
2.3 Preprocessing Stage	p. 43
2.3.1 Building a model	p. 43
2.3.1.1 Defining element types and real constants	p. 44
2.3.1.2 Defining material properties	p. 46
2.3.2 Construction of the model	p. 47
2.3.2.1 Creating the model geometry	p. 47
2.3.2.2 Applying loads	p. 48
2.4 Solution Stage	p. 49
2.5 Postprocessing Stage	p. 50
Chapter 3 Application of ANSYS to Stress Analysis	p. 51
3.1 Cantilever beam	p. 51
3.1.1 Example problem: A cantilever beam	p. 52
3.1.2 Problem description	p. 53
3.1.2.1 Review of the solutions obtained by the elementary beam theory	p. 53
3.1.3 Analytical procedures	p. 53
3.1.3.1 Creation of an analytical model	p. 53
3.1.3.2 Input of the elastic properties of the beam material	p. 56
3.1.3.3 Finite-element discretization of the beam area	p. 57
3.1.3.4 Input of boundary conditions	p. 62
3.1.3.5 Solution procedures	p. 71
3.1.3.6 Graphical representation of the results	p. 73
3.1.4 Comparison of FEM results with experimental ones	p. 76
3.1.5 Problems to solve	p. 76
Appendix Procedures for Creating Stepped Beams	p. 80
A3.1 Creation of a stepped beam	p. 80
A3.1.1 How to cancel the selection of areas	p. 81
A3.2 Creation of a stepped beam with a rounded fillet	p. 81
A3.2.1 How to display area numbers	p. 84
3.2 The Principle of St. Venant	p. 84
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	p. 84
3.2.2 Problem description	p. 85
3.2.3 Analytical procedures	p. 85
3.2.3.1 Creation of an analytical model	p. 85
3.2.3.2 Input of the elastic properties of the strip material	p. 86
3.2.3.3 Finite-element discretization of the strip area	p. 86
3.2.3.4 Input of boundary conditions	p. 88
3.2.3.5 Solution procedures	p. 89
3.2.3.6 Contour plot of stress	p. 92
3.2.4 Discussion	p. 92
3.3 Stress Concentration Due to Elliptic Holes	p. 93
3.3.1 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	p. 93
3.3.2 Problem description	p. 94
3.3.3 Analytical procedures	p. 94
3.3.3.1 Creation of an analytical model	p. 94
3.3.3.2 Input of the elastic properties of the plate material	p. 97
3.3.3.3 Finite-element discretization of the quarter plate area	p. 98
3.3.3.4 Input of boundary conditions	p. 99
3.3.3.5 Solution procedures	p. 100
3.3.3.6 Contour plot of stress	p. 101
3.3.3.7 Observation of the variation of the longitudinal stress distribution in the ligament region	p. 101
3.3.4 Discussion	p. 102
3.3.5 Problems to solve	p. 105
3.4 Stress Singularity Problem	p. 106
3.4.1 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	p. 106
3.4.2 Problem description	p. 106
3.4.3 Analytical procedures	p. 107
3.4.3.1 Creation of an analytical model	p. 107
3.4.3.2 Input of the elastic properties of the plate material	p. 110
3.4.3.3 Finite-element discretization of the centercracked tension plate area	p. 110
3.4.3.4 Input of boundary conditions	p. 113
3.4.3.5 Solution procedures	p. 114
3.4.3.6 Contour plot of stress	p. 115
3.4.4 Discussion	p. 116
3.4.5 Problems to solve	p. 118
3.5 Two-Dimensional Contact Stress	p. 120
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 force	p. 120
3.5.2 Problem description	p. 120
3.5.3 Analytical procedures	p. 121
3.5.3.1 Creation of an analytical model	p. 121
3.5.3.2 Input of the elastic properties of the material for the cylinder and the flat plate	p. 123
3.5.3.3 Finite-element discretization of the cylinder and the flat plate areas	p. 123
3.5.3.4 Input of boundary conditions	p. 133
3.5.3.5 Solution procedures	p. 135
3.5.3.6 Contour plot of stress	p. 135
3.5.4 Discussion	p. 136
3.5.5 Problems to solve	p. 138
References	p. 141
Chapter 4 Mode Analysis	p. 143
4.1 Introduction	p. 143
4.2 Mode Analysis of A Straight Bar	p. 144
4.2.1 Problem description	p. 144
4.2.2 Analytical solution	p. 144
4.2.3 Model for finite-element analysis	p. 145
4.2.3.1 Element type selection	p. 145
4.2.3.2 Real constants for beam element	p. 147
4.2.3.3 Material properties	p. 147
4.2.3.4 Create keypoints	p. 149
4.2.3.5 Create a line for beam element	p. 151
4.2.3.6 Create mesh in a line	p. 152
4.2.3.7 Boundary conditions	p. 154
4.2.4 Execution of the analysis	p. 157
4.2.4.1 Definition of the type of analysis	p. 157
4.2.4.2 Execute calculation	p. 159
4.2.5 Postprocessing	p. 161
4.2.5.1 Read the calculated results of the first mode of vibration	p. 161
4.2.5.2 Plot the calculated results	p. 161
4.2.5.3 Read the calculated results of the second and third modes of vibration	p. 161
4.3 Mode Analysis of a Suspension for Hard-Disc Drive	p. 163
4.3.1 Problem description	p. 163
4.3.2 Create a model for analysis	p. 163
4.3.2.1 Element type selection	p. 163
4.3.2.2 Real constants for beam element	p. 165
4.3.2.3 Material properties	p. 168
4.3.2.4 Create keypoints	p. 168
4.3.2.5 Create areas for suspension	p. 171
4.3.2.6 Boolean operation	p. 175
4.3.2.7 Create mesh in areas	p. 177
4.3.2.8 Boundary conditions	p. 179
4.3.3 Analysis	p. 182
4.3.3.1 Define the type of analysis	p. 182
4.3.3.2 Execute calculation	p. 182
4.3.4 Postprocessing	p. 183
4.3.4.1 Read the calculated results of the first mode of vibration	p. 183
4.3.4.2 Plot the calculated results	p. 183
4.3.4.3 Read the calculated results of higher modes of vibration	p. 184
4.4 Mode Analysis of a One-Axis Precision Moving Table Using Elastic Hinges	p. 188
4.4.1 Problem description	p. 188
4.4.2 Create a model for analysis	p. 189
4.4.2.1 Select element type	p. 189
4.4.2.2 Material properties	p. 189
4.4.2.3 Create keypoints	p. 192
4.4.2.4 Create areas for the table	p. 193
4.4.2.5 Create mesh in areas	p. 197
4.4.2.6 Boundary conditions	p. 201
4.4.3 Analysis	p. 205
4.4.3.1 Define the type of analysis	p. 205
4.4.3.2 Execute calculation	p. 208
4.4.4 Postprocessing	p. 209
4.4.4.1 Read the calculated results of the first mode of vibration	p. 209
4.4.4.2 Plot the calculated results	p. 209
4.4.4.3 Read the calculated results of the second and third modes of vibration	p. 210
4.4.4.4 Animate the vibration mode shape	p. 211
Chapter 5 Analysis For Fluid Dynamics	p. 215
5.1 Introduction	p. 215
5.2 Analysis of Flow Structure in A Diffuser	p. 216
5.2.1 Problem description	p. 216
5.2.2 Create a model for analysis	p. 216
5.2.2.1 Select kind of analysis	p. 216
5.2.2.2 Element type selection	p. 217
5.2.2.3 Create keypoints	p. 219
5.2.2.4 Create areas for diffuser	p. 221
5.2.2.5 Create mesh in lines and areas	p. 222
5.2.2.6 Boundary conditions	p. 226
5.2.3 Execution of the analysis	p. 231
5.2.3.1 Flotran set up	p. 231
5.2.4 Execute calculation	p. 233
5.2.5 Postprocessing	p. 234
5.2.5.1 Read the calculated results of the first mode of vibration	p. 234
5.2.5.2 Plot the calculated results	p. 234
5.2.5.3 Plot the calculated results by path operation	p. 237
5.3 Analysis of flow structure in a channel with a butterfly Valve	p. 242
5.3.1 Problem description	p. 242
5.3.2 Create a model for analysis	p. 242
5.3.2.1 Select kind of analysis	p. 242
5.3.2.2 Select element type	p. 243
5.3.2.3 Create keypoints	p. 243
5.3.2.4 Create areas for flow channel	p. 245
5.3.2.5 Subtract the valve area from the channel area	p. 245
5.3.2.6 Create mesh in lines and areas	p. 246
5.3.2.7 Boundary conditions	p. 248
5.3.3 Execution of the analysis	p. 251
5.3.3.1 Flotran set up	p. 251
5.3.4 Execute calculation	p. 253
5.3.5 Postprocessing	p. 254
5.3.5.1 Read the calculated results	p. 254
5.3.5.2 Plot the calculated results	p. 255
5.3.5.3 Detailed view of the calculated flow velocity	p. 256
5.3.5.4 Plot the calculated results by path operation	p. 259
Chapter 6 Application of ANSYS to Thermo Mechanics	p. 263
6.1 General characteristic of heat transfer problems	p. 263
6.2 Heat transfer through two walls	p. 265
6.2.1 Problem description	p. 265
6.2.2 Construction of the model	p. 265
6.2.3 Solution	p. 276
6.2.4 Postprocessing	p. 280
6.3 Steady-State Thermal Analysis of a Pipe Intersection	p. 285
6.3.1 Description of the problem	p. 285
6.3.2 Preparation for model building	p. 288
6.3.3 Construction of the model	p. 291
6.3.4 Solution	p. 298
6.3.5 Postprocessing stage	p. 306
6.4 Heat Dissipation Through Ribbed Surface	p. 312
6.4.1 Problem description	p. 312
6.4.2 Construction of the model	p. 313
6.4.3 Solution	p. 321
6.4.4 Postprocessing	p. 325
Chapter 7 Application of ANSYS to Contact Between Machine Elements	p. 331
7.1 General Characteristics of Contact Problems	p. 331
7.2 Example Problems	p. 332
7.2.1 Pin-in-hole interference fit	p. 332
7.2.1.1 Problem description	p. 332
7.2.1.2 Construction of the model	p. 333
7.2.1.3 Material properties and element type	p. 338
7.2.1.4 Meshing	p. 339
7.2.1.5 Creation of contact pair	p. 342
7.2.1.6 Solution	p. 347
7.2.1.7 Postprocessing	p. 352
7.2.2 Concave contact between cylinder and two blocks	p. 359
7.2.2.1 Problem description	p. 359
7.2.2.2 Model construction	p. 360
7.2.2.3 Material properties	p. 365
7.2.2.4 Meshing	p. 368
7.2.2.5 Creation of contact pair	p. 372
7.2.2.6 Solution	p. 374
7.2.2.7 Postprocessing	p. 379
7.2.3 Wheel-on-rail line contact	p. 382
7.2.3.1 Problem description	p. 382
7.2.3.2 Model construction	p. 385
7.2.3.3 Properties of material	p. 391
7.2.3.4 Meshing	p. 392
7.2.3.5 Creation of contact pair	p. 398
7.2.3.6 Solution	p. 401
7.2.3.7 Postprocessing	p. 404
7.2.4 0-ring assembly	p. 410
7.2.4.1 Problem description	p. 410
7.2.4.2 Model construction	p. 412
7.2.4.3 Selection of materials	p. 413
7.2.4.4 Geometry of the assembly and meshing	p. 423
7.2.4.5 Creating contact interface	p. 427
7.2.4.6 Solution	p. 436
7.2.4.7 Postprocessing (first load step)	p. 442
7.2.4.8 Solution (second load step)	p. 444
7.2.4.9 Postprocessing (second load step)	p. 451
Index	p. 453

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