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Copyright, ii
Preface, xi
Acknowledgments, xv
1. Introduction, 1
1.1. Engineering Problems, 2
1.2. Numerical Methods, 5
1.3. A Brief History of the Finite Element Method and ANSYS, 6
1.4. Basic Steps in the Finite Element Method, 6
1.5. Direct Formulation, 8
1.6. Minimum Total Potential Energy Formulation, 37
1.7. Weighted Residual Formulations, 43
1.8. Verification of Results, 48
1.9. Understanding the Problem, 49
Summary, 53
References, 54
Problems, 54
2. Matrix Algebra, 66
2.1. Basic Definitions, 66
2.2. Matrix Addition or Subtraction, 69
2.3. Matrix Multiplication, 69
2.4. Partitioning of a Matrix, 73
2.5. Transpose of a Matrix, 77
2.6. Determinant of a Matrix, 81
2.7. Solutions of Simultaneous Linear Equations, 86
2.8. Inverse of a Matrix, 94
2.9. Eigenvalues and Eigenvectors, 98
2.10. Using MATLAB to Manipulate Matrices, 102
2.11. Using Excel to Manipulate Matrices, 106
Summary, 112
References, 113
Problems, 113
3. Trusses, 117
3.1. Definition of a Truss, 117
3.2. Finite Element Formulation, 118
3.3. Space Trusses, 135
3.4. Overview of the ANSYS Program, 137
3.5. Examples Using ANSYS, 144
3.6. Verification of Results, 177
Summary, 179
References, 179
Problems, 179
4. Axial Members, Beams, and Frames, 189
4.1. Members Under Axial Loading, 189
4.2. Beams, 197
4.3. Finite Element Formulation of Beams, 202
4.4. Finite Element Formulation of Frames, 213
4.5. Three-Dimensional Beam Element, 219
4.6. An Example Using ANSYS, 222
4.7. Verification of Results, 236
Summary, 238
References, 239
Problems, 240
5. One-Dimensional Elements, 252
5.1. Linear Elements, 252
5.2. Quadratic Elements, 256
5.3. Cubic Elements, 258
5.4. Global, Local, and Natural Coordinates, 261
5.5. Isoparametric Elements, 263
5.6. Numerical Integration: Gauss–Legendre Quadrature, 265
5.7. Examples of One-Dimensional Elements in ANSYS, 270
Summary, 270
References, 270
Problems, 270
6. Analysis of One-Dimensional Problems, 277
6.1. Heat Transfer Problems, 277
6.2. A Fluid Mechanics Problem, 292
6.3. An Example Using ANSYS, 296
6.4. Verification of Results, 311
Summary, 312
References, 312
Problems, 313
7. Two-Dimensional Elements, 316
7.1. Rectangular Elements, 316
7.2. Quadratic Quadrilateral Elements, 320
7.3. Linear Triangular Elements, 325
7.4. Quadratic Triangular Elements, 330
7.5. Axisymmetric Elements, 334
7.6. Isoparametric Elements, 339
7.7. Two-Dimensional Integrals: Gauss–Legendre Quadrature, 341
7.8. Examples of Two-Dimensional Elements in ANSYS, 344
Summary, 345
References, 345
Problems, 346
8. More ANSYS, 353
8.1. ANSYS Program, 353
8.2. ANSYS Database and Files, 354
8.3. Creating a Finite Element Model with ANSYS: Preprocessing, 356
8.4. h-Method Versus p-Method, 370
8.5. Applying Boundary Conditions, Loads, and the Solution, 370
8.6. Results of Your Finite Element Model: Postprocessing, 373
8.7. Selection Options, 378
8.8. Graphics Capabilities, 379
8.9. Error-Estimation Procedures, 381
8.10. An Example Problem, 383
Summary, 397
References, 398
9. Analysis of Two-Dimensional Heat Transfer Problems, 405
9.1. General Conduction Problems, 405
9.2. Formulation with Rectangular Elements, 412
9.3. Formulation with Triangular Elements, 423
9.4. Axisymmetric Formulation of Three-Dimensional Problems, 434
9.5. Unsteady Heat Transfer, 442
9.6. Conduction Elements Used by ANSYS, 452
9.7. Examples Using ANSYS, 453
9.8. Verification of Results, 491
Summary, 491
References, 493
Problems, 493
10. Analysis of Two-Dimensional Solid Mechanics Problems, 505
10.1. Torsion of Members with Arbitrary Cross-Section Shape, 505
10.2. Plane-Stress Formulation, 515
10.3. Isoparametric Formulation: Using a Quadrilateral Element, 523
10.4. Axisymmetric Formulation, 530
10.5. Basic Failure Theories, 532
10.6. Examples Using ANSYS, 533
10.7. Verification of Results, 554
Summary, 554
References, 556
Problems, 556
11. Dynamic Problems, 565
11.1. Review of Dynamics, 565
11.2. Review of Vibration of Mechanical and Structural Systems, 579
11.3. Lagrange’s Equations, 596
11.4. Finite Element Formulation of Axial Members, 598
11.5. Finite Element Formulation of Beams and Frames, 602
11.6. Examples Using ANSYS, 616
Summary, 636
References, 636
Problems, 636
12. Analysis of Fluid Mechanics Problems, 643
12.1. Direct Formulation of Flow Through Pipes, 643
12.2. Ideal Fluid Flow, 649
12.3. Groundwater Flow, 655
12.4. Examples Using ANSYS, 658
12.5. Verification of Results, 679
Summary, 680
References, 681
Problems, 682
13. Three-Dimensional Elements, 687
13.1. The Four-Node Tetrahedral Element, 687
13.2. Analysis of Three-Dimensional Solid Problems Using Four-Node Tetrahedral Elements, 690
13.3. The Eight-Node Brick Element, 695
13.4. The Ten-Node Tetrahedral Element, 697
13.5. The Twenty-Node Brick Element, 698
13.6. Examples of Three-Dimensional Elements in ANSYS, 700
13.7. Basic Solid-Modeling Ideas, 704
13.8. A Thermal Example Using ANSYS, 715
13.9. A Structural Example Using ANSYS, 732
Summary, 745
References, 745
Problems, 745
14. Design and Material Selection, 754
14.1. Engineering Design Process, 755
14.2. Material Selection, 758
14.3. Electrical, Mechanical, and Thermophysical Properties of Materials, 759
14.4. Common Solid Engineering Materials, 761
14.5. Some Common Fluid Materials, 768
Summary, 770
Reference, 770
Problems, 770
15. Design Optimization, 772
15.1. Introduction to Design Optimization, 772
15.2. The Parametric Design Language of ANSYS, 776
15.3. Examples of Batch Files, 778
15.4. An Example of an Optimization Batch Files, 792
Summary, 800
References, 800
Problems, 800
Appendix A. Mechanical Properties of Some Materials, 801
Appendix B. Thermophysical Properties of Some Materials, 804
Appendix C. Properties of Common Line and Area Shapes, 805
Appendix D. Geometric Properties of Structural Steel Shapes, 808
Appendix E. Conversion Factors, 812
Appendix F. An Introduction to MATLAB, 814
Index, 849

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