Finite Element Analysis: Theory and Application with ANSYS

Cover......Page 1
Title......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 14
Acknowledgments......Page 18
1 Introduction......Page 22
 1.1 Engineering Problems......Page 23
 1.2 Numerical Methods......Page 26
 1.4 Basic Steps in the Finite Element Method......Page 27
 1.5 Direct Formulation......Page 29
 1.6 Minimum Total Potential Energy Formulation......Page 58
 1.7 Weighted Residual Formulations......Page 64
 1.8 Verification of Results......Page 69
 1.9 Understanding the Problem......Page 70
 Problems......Page 75
 2.1 Basic Definitions......Page 87
 2.3 Matrix Multiplication......Page 90
 2.4 Partitioning of a Matrix......Page 94
 2.5 Transpose of a Matrix......Page 98
 2.6 Determinant of a Matrix......Page 102
 2.7 Solutions of Simultaneous Linear Equations......Page 107
 2.8 Inverse of a Matrix......Page 115
 2.9 Eigenvalues and Eigenvectors......Page 119
 2.10 Using Matlab to Manipulate Matrices......Page 123
 2.11 Using Excel to Manipulate Matrices......Page 127
 Summary......Page 141
 Problems......Page 142
 3.1 Definition of a Truss......Page 146
 3.2 Finite Element Formulation......Page 147
 3.3 Space Trusses......Page 172
 3.4 Overview of the Ansys Program......Page 174
 3.5 Examples Using Ansys......Page 182
 3.6 Verification of Results......Page 214
 Problems......Page 216
 4.1 Members Under Axial Loading......Page 226
 4.2 Beams......Page 234
 4.3 Finite Element Formulation of Beams......Page 239
 4.4 Finite Element Formulation of Frames......Page 255
 4.5 Three-Dimensional Beam Element......Page 261
 4.6 An Example Using Ansys......Page 263
 4.7 Verification of Results......Page 288
 Summary......Page 290
 References......Page 291
 Problems......Page 292
 5.1 Linear Elements......Page 304
 5.2 Quadratic Elements......Page 308
 5.3 Cubic Elements......Page 310
 5.4 Global, Local, and Natural Coordinates......Page 313
 5.5 Isoparametric Elements......Page 315
 5.6 Numerical Integration: Gauss–Legendre Quadrature......Page 317
 Problems......Page 322
 6.1 Heat Transfer Problems......Page 329
 6.2 A Fluid Mechanics Problem......Page 348
 6.3 An Example Using Ansys......Page 352
 6.4 Verification of Results......Page 367
 References......Page 368
 Problems......Page 369
 7.1 Rectangular Elements......Page 372
 7.2 Quadratic Quadrilateral Elements......Page 376
 7.3 Linear Triangular Elements......Page 381
 7.4 Quadratic Triangular Elements......Page 386
 7.5 Axisymmetric Elements......Page 390
 7.6 Isoparametric Elements......Page 395
 7.7 Two-Dimensional Integrals: Gauss–Legendre Quadrature......Page 398
 7.8 Examples of Two-Dimensional Elements in Ansys......Page 399
 References......Page 400
 Problems......Page 401
 8.1 Ansys Program......Page 408
 8.2 Ansys Database and Files......Page 409
 8.3 Creating a Finite Element Model with Ansys: Preprocessing......Page 411
 8.5 Applying Boundary Conditions, Loads, and the Solution......Page 425
 8.6 Results of Your Finite Element Model: Postprocessing......Page 428
 8.7 Selection Options......Page 433
 8.8 Graphics Capabilities......Page 434
 8.9 Error-Estimation Procedures......Page 436
 8.10 An Example Problem......Page 438
 Summary......Page 452
 References......Page 453
 9.1 General Conduction Problems......Page 454
 9.2 Formulation with Rectangular Elements......Page 461
 9.3 Formulation with Triangular Elements......Page 472
 9.4 Axisymmetric Formulation of Three-Dimensional Problems......Page 491
 9.5 Unsteady Heat Transfer......Page 498
 9.6 Conduction Elements Used by Ansys......Page 508
 9.7 Examples Using Ansys......Page 509
 Summary......Page 549
 Problems......Page 551
 10.1 Torsion of Members with Arbitrary Cross-Section Shape......Page 563
 10.2 Plane-Stress Formulation......Page 579
 10.3 Isoparametric Formulation: Using a Quadrilateral Element......Page 587
 10.4 Axisymmetric Formulation......Page 594
 10.5 Basic Failure Theories......Page 596
 10.6 Examples Using Ansys......Page 597
 Summary......Page 619
 Problems......Page 621
 11.1 Review of Dynamics......Page 630
 11.2 Review of Vibration of Mechanical and Structural Systems......Page 644
 11.3 Lagrange’s Equations......Page 661
 11.4 Finite Element Formulation of Axial Members......Page 663
 11.5 Finite Element Formulation of Beams and Frames......Page 672
 11.6 Examples Using Ansys......Page 686
 Problems......Page 705
 12.1 Direct Formulation of Flow Through Pipes......Page 712
 12.2 Ideal Fluid Flow......Page 724
 12.3 Groundwater Flow......Page 730
 12.4 Examples Using Ansys......Page 733
 12.5 Verification of Results......Page 754
 Summary......Page 755
 References......Page 756
 Problems......Page 757
 13.1 The Four-NodeTetrahedral Element......Page 762
 13.2 Analysis of Three-Dimensional Solid Problems Using Four-NodeTetrahedral Elements......Page 765
 13.3 The Eight-Node Brick Element......Page 770
 13.4 The Ten-Node Tetrahedral Element......Page 772
 13.5 The Twenty-Node Brick Element......Page 773
 13.6 Examples of Three-Dimensional Elements in Ansys......Page 775
 13.7 Basic Solid-Modeling Ideas......Page 779
 13.8 A Thermal Example Using Ansys......Page 790
 13.9 A Structural Example Using Ansys......Page 807
 Problems......Page 820
14 Design and Material Selection......Page 829
 14.1 Engineering Design Process......Page 830
 14.2 Material Selection......Page 833
 14.3 Electrical, Mechanical, and Thermophysical Properties of Materials......Page 834
 14.4 Common Solid Engineering Materials......Page 836
 14.5 Some Common Fluid Materials......Page 843
 Problems......Page 845
 15.1 Introduction to Design Optimization......Page 847
 15.2 The Parametric Design Language of Ansys......Page 851
 15.3 Examples of Batch Files......Page 853
 Summary......Page 864
 Problems......Page 865
Appendix A Mechanical Properties of Some Materials......Page 866
Appendix B Thermophysical Properties of Some Materials......Page 870
Appendix C Properties of Common Line and Area Shapes......Page 872
Appendix D Geometrical Properties of Structural Steel Shapes......Page 876
Appendix EConversion Factors......Page 880
Appendix F An Introduction to MATLAB......Page 882
 A......Page 916
 B......Page 917
 D......Page 918
 E......Page 919
 F......Page 920
 G......Page 921
 I......Page 922
 M......Page 923
 P......Page 925
 S......Page 926
 T......Page 927
 Y......Page 929