Title Details

Preface v

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 ElementModeling Techniques 281

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

Pro/Engineer 333

A.1. 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.1. 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.1. 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.1. 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