Introduction to Finite Element Analysis and Design

Introduction to Finite Element Analysis and Design
Nam-Ho Kim, Bhavani V. Sankar
Contents
Preface vii
Chapter 0. Mathematical Preliminaries 1
0.1. Vectors and Matrices 1
0.2. Vector-Matrix Calculus 3 \
0.3. Matrix Equations 8
0.4. Eigen Values and Eigen Vectors 8
0.5. Quadratic Forms 12
0.6. Maxima and Minima of Functions ! 13
0.7. Exercise 14
Chapter 1. Stress-Strain Analysis 17
1.1. Stress 17
1.2. Strain 30
1.3. Stress-Strain Relations 35
1.4. Boundary Value Problems’- 39
1.5. Failure Theories 43
1.6. Safety Factor 49
1.7. Exercise 52
Chapter 2. Uniaxial Bar and Truss
Elements-Direct Method 60
2.1. Illustration of the Direct Method 61
2.2. Uniaxial Bar Element 66
2.3. Plane Truss Elements 73
2.4. Three-Dimensional Truss Elements
(Space Truss) 83
2.5. Thermal Stresses 87
2.6. Projects 94
2.7. Exercise 98
Chapter 3. Weighted Residual and Energy
Methods for One-Dimensional
Problems 108
3.1. Exact vs. Approximate Solution 108
3.2. Galerkin Method 109
3.3. Higher-Order Differential
Equations 114
3.4. Finite Element Approximation 117
3.5. Formal Procedure 124
3.6. Energy Methods 129
3.7. Exercise 138
Chapter 4. Finite Element Analysis of Beams
and Frames 143
4.1. Review of Elementary Beam Theory 143
4.2. Rayleigh-Ritz Method 148
4.3. Finite Element Interpolation 153
4.4. Finite Element Equation for the Beam
Element 158
4.5. Bending Moment and Shear Force
Distribution 166
4.6. Plane Frame 171
4.7. Project 175
4.8. Exercise 176
Chapter 5. Finite Elements for Heat Transfer
Problems 185
5.1. Introduction 185
5.2. Fourier Heat Conduction Equation 186
5.3. Finite Element Anlaysis – Direct
Method 188
5.4. Galerkin Method for Heat Conduction
Problems 194
5.5. Convection Boundary Conditions 200
5.6. Exercise 207
Chapter 6. Finite Elements for Plane
Solids 211
6.1. Introduction 211
6.2. Types of Two-Dimensional
Problems 211
6.3. Principle of Minimum Potential
Energy 214
6.4. Constant Strain Triangular (CST)
Element 216
6.5. Four-Node Rectangular Element 229
6.6. Four-Node Iso-Parametric Quadrilateral
Element 237
6.7. Numerical Integration 248
6.8. Project 253
6.9. Exercise 254
Chapter 7. Finite Element Procedures and
Modeling 261
7.1. Finite Element Analysis Procedures 261
7.2. Finite Element Modeling Techniques 281
xixii Contents
7.3. Project 291
7.4. Exercise 292
Chapter 8. Structural Design Using Finite
Elements 297
8.1. Introduction 297
8.2. Safety Margin in Design 298
8.3. Intuitive Design: Fully-Stressed
Design 301
8.4. Design Parameterization 304
8.5. Parameter Study – Sensitivity
Analysis 307
8.6. Structural Optimization 313
8.7. Project: Design Optimization of a
Bracket 325
8.8. Exercise 327
Appendix A. Finite Element Analysis Using
ProZEngineer 333
A.l. Introduction 333
A.2. Getting Start 333
A.3. Plate with a Hole Analysis 334
A.4. Design Sensitivity Analysis/Parameter
Study 339
A.5. Design Optimization 341
Appendix B. Finite Element Analysis Using
NEi Nastran 343
B.l. Introduction 343
B.2. Getting Start 343
B.3. Plate with a Hole Analysis 343
B.4. Static Analysis of Beams 350
B.5. Examples in the text 356
Appendix C. Finite Element Analysis Using
ANSYS 363
C.l. Introduction 363
C.2. Getting Start 364
C.3. Static Analysis of a Corner
Bracket 365
C.4. Examples in the Text 381
Appendix D. Finite Element Analysis Using
MATLAB Toolbox 391
D.l. Finite Element Analysis of Bar and
Truss 391
D.2. Finite Element Analysis Using Frame
Elements 403
D.3. Finite Element Analysis Using Plane
Solid Elements 408
Index 417

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