# Finite Element Analysis Theory and Application with ANSYS PDF

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Contents

## Finite Element Analysis Theory and Application with ANSYS PDF

While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively.

Teaching and Learning Experience

This program will provide a better teaching and learning experience—for you and your students. It will help:

• Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students.
• Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book.
• Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help students apply concepts.

## Contents

Preface 13 – Finite Element Analysis Theory and Application with ANSYS PDF
Acknowledgments 17
1 Introduction 21
1.1 Engineering Problems 22
1.2 Numerical Methods 25
1.3 A Brief History of the Finite Element Method and Ansys 26
1.4 Basic Steps in the Finite Element Method 26
1.5 Direct Formulation 28
1.6 Minimum Total Potential Energy Formulation 57
1.7 Weighted Residual Formulations 63
1.8 Verification of Results 68
1.9 Understanding the Problem 69
Summary 74
References 74
Problems 74
2 Matrix Algebra 86
2.1 Basic Definitions 86
2.2 Matrix Addition or Subtraction 89
2.3 Matrix Multiplication 89
2.4 Partitioning of a Matrix 93
2.5 Transpose of a Matrix 97
2.6 Determinant of a Matrix 101
2.7 Solutions of Simultaneous Linear Equations 106
2.8 Inverse of a Matrix 114
2.9 Eigenvalues and Eigenvectors 118
2.10 Using Matlab to Manipulate Matrices 122
2.11 Using Excel to Manipulate Matrices 126
Summary 140 – Finite Element Analysis Theory and Application with ANSYS PDF
References 141
Problems 141
3 Trusses 145
3.1 Definition of a Truss 145
3.2 Finite Element Formulation 146
3.3 Space Trusses 171

3.4 Overview of the Ansys Program 173
3.5 Examples Using Ansys 181
3.6 Verification of Results 213
Summary 215
References 215
Problems 215
4 Axial Members, Beams, and Frames 225
4.2 Beams 233
4.3 Finite Element Formulation of Beams 238
4.4 Finite Element Formulation of Frames 254
4.5 Three-Dimensional Beam Element 260
4.6 An Example Using Ansys 262
4.7 Verification of Results 287
Summary 289
References 290
Problems 291
5 One-Dimensional Elements 303
5.1 Linear Elements 303
5.3 Cubic Elements 309
5.4 Global, Local, and Natural Coordinates 312
5.5 Isoparametric Elements 314
5.6 Numerical Integration: Gauss–Legendre Quadrature 316
5.7 Examples of One-Dimensional Elements in Ansys 321
Summary 321 – Finite Element Analysis Theory and Application with ANSYS PDF
References 321
Problems 321
6 Analysis of One-Dimensional Problems 328
6.1 Heat Transfer Problems 328
6.2 A Fluid Mechanics Problem 347
6.3 An Example Using Ansys 351
6.4 Verification of Results 366
Summary 367
References 367
Problems 368
7 ­Two-Dimensional Elements 371
7.1 Rectangular Elements 371

7.3 Linear Triangular Elements 380
7.5 Axisymmetric Elements 389
7.6 Isoparametric Elements 394
7.7 Two-Dimensional Integrals: Gauss–Legendre Quadrature 397
7.8 Examples of Two-Dimensional Elements in Ansys 398
Summary 399
References 399
Problems 400 – Finite Element Analysis Theory and Application with ANSYS PDF
8 More Ansys 407
8.1 Ansys Program 407
8.2 Ansys Database and Files 408
8.3 Creating a Finite Element Model with Ansys: Preprocessing 410
8.4 h-Method Versus p-Method 424
8.5 Applying Boundary Conditions, Loads, and the Solution 424
8.6 Results of Your Finite Element Model: Postprocessing 427
8.7 Selection Options 432
8.8 Graphics Capabilities 433
8.9 Error-Estimation Procedures 435
8.10 An Example Problem 437
Summary 451
References 452
9 Analysis of ­Two-Dimensional Heat Transfer Problems 453
9.1 General Conduction Problems 453
9.2 Formulation with Rectangular Elements 460
9.3 Formulation with Triangular Elements 471
9.4 Axisymmetric Formulation of Three-Dimensional Problems 490
9.6 Conduction Elements Used by Ansys 507
9.7 Examples Using Ansys 508
9.8 Verification of Results 548
Summary 548
References 550
Problems 550 – Finite Element Analysis Theory and Application with ANSYS PDF
10 Analysis of ­Two-Dimensional Solid Mechanics Problems 562
10.1 Torsion of Members with Arbitrary Cross-Section Shape 562
10.2 Plane-Stress Formulation 578
10.3 Isoparametric Formulation: Using a Quadrilateral Element 586
10.4 Axisymmetric Formulation 593
10.5 Basic Failure Theories 595

10.6 Examples Using Ansys 596
10.7 Verification of Results 618
Summary 618
References 620
Problems 620
11 Dynamic Problems 629
11.1 Review of Dynamics 629
11.2 Review of Vibration of Mechanical and Structural Systems 643
11.3 Lagrange’s Equations 660
11.4 Finite Element Formulation of Axial Members 662
11.5 Finite Element Formulation of Beams and Frames 671
11.6 Examples Using Ansys 685
Summary 704
References 704
Problems 704
12 Analysis of Fluid Mechanics Problems 711
12.1 Direct Formulation of Flow Through Pipes 711
12.2 Ideal Fluid Flow 723
12.3 Groundwater Flow 729
12.4 Examples Using Ansys 732
12.5 Verification of Results 753
Summary 754 – Finite Element Analysis Theory and Application with ANSYS PDF
References 755
Problems 756
13 ­Three-Dimensional Elements 761
13.1 The Four-Node Tetrahedral Element 761
13.2 Analysis of Three-Dimensional Solid Problems Using Four-Node
Tetrahedral Elements 764
13.3 The Eight-Node Brick Element 769
13.4 The Ten-Node Tetrahedral Element 771
13.5 The Twenty-Node Brick Element 772
13.6 Examples of Three-Dimensional Elements in Ansys 774
13.7 Basic Solid-Modeling Ideas 778
13.8 A Thermal Example Using Ansys 789
13.9 A Structural Example Using Ansys 806
Summary 819
References 819
Problems 819

14 Design and Material Selection 828
14.1 Engineering Design Process 829
14.2 Material Selection 832
14.3 Electrical, Mechanical, and Thermophysical Properties of Materials 833
14.4 Common Solid Engineering Materials 835
14.5 Some Common Fluid Materials 842
Summary 844 – Finite Element Analysis Theory and Application with ANSYS PDF
References 844
Problems 844
15 Design Optimization 846
15.1 Introduction to Design Optimization 846
15.2 The Parametric Design Language of Ansys 850
15.3 Examples of Batch Files 852
Summary 863
References 864
Problems 864
Appendix A Mechanical Properties of Some Materials 865
Appendix B Thermophysical Properties of Some Materials 869
Appendix C Properties of Common Line and Area Shapes 871
Appendix D Geometrical Properties of Structural Steel Shapes 875
Appendix E Conversion Factors 879
Appendix F An Introduction to MATLAB 881
Index 915

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