Finite Element Analysis: Theory and Application with ANSYS

For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering.   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.

Table of Contents:
 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 54  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 120  References 121  Problems 121  3 Trusses 125  3.1 Definition of a Truss 125  3.2 Finite Element Formulation 126  3.3 Space Trusses 151  3.4 Overview of the ANSYS Program 153  3.5 Examples Using ANSYS 161  3.6 Verification of Results 193  Summary 195  References 195  Problems 195  4 Axial members, Beams, and Frames 205  4.1 Members Under Axial Loading 205  4.2 Beams 213  4.3 Finite Element Formulation of Beams 218  4.4 Finite Element Formulation of Frames 234  4.5 Three- Dimensional Beam Element 240  4.6 An Example Using ANSYS 242  4.7 Verification of Results 267  Summary 269  References 270  Problems 271  5 One- Dimensional Elements 283  5.1 Linear Elements 283  5.2 Quadratic Elements 287  5.3 Cubic Elements 289  5.4 Global, Local, and Natural Coordinates 292  5.5 Isoparametric Elements 294  5.6 Numerical Integration: Gauss–Legendre Quadrature 296  5.7 Examples of One- Dimensional Elements in ANSYS 301  Summary 301  References 301  Problems 301  6 Analysis of One- Dimensional Problems 308  6.1 Heat Transfer Problems 308  6.2 A Fluid Mechanics Problem 327  6.3 An Example Using ANSYS 331  6.4 Verification of Results 346  Summary 347  References 347  Problems 348  7 Two- Dimensional Elements 351  7.1 Rectangular Elements 351  7.2 Quadratic Quadrilateral Elements 355  7.3 Linear Triangular Elements 360  7.4 Quadratic Triangular Elements 365  7.5 Axisymmetric Elements 369  7.6 Isoparametric Elements 374  7.7 Two- Dimensional Integrals: Gauss—Legendre Quadrature 377  7.8 Examples of Two- Dimensional Elements in ANSYS 378  Summary 379  References 379  Problems 380  8 More Ansys 387  8.1 ANSYS Program 387  8.2 ANSYS Database and Files 388  8.3 Creating a Finite Element Model with ANSYS: Preprocessing 390  8.4 h- Method Versus p- Method 404  8.5 Applying Boundary Conditions, Loads, and the Solution 404  8.6 Results of Your Finite Element Model: Postprocessing 407  8.7 Selection Options 412  8.8 Graphics Capabilities 413  8.9 Error- Estimation Procedures 415  8.10 An Example Problem 417  Summary 431  References 432  9 Analysis of Two- Dimensional Heat Transfer Problems 433  9.1 General Conduction Problems 433  9.2 Formulation with Rectangular Elements 440  9.3 Formulation with Triangular Elements 451  9.4 Axisymmetric Formulation of Three- Dimensional Problems 470  9.5 Unsteady Heat Transfer 477  9.6 Conduction Elements used by ANSYS 487  9.7 Examples Using ANSYS 488  9.8 Verification of Results 528  Summary 528  References 530  Problems 530  10 Analysis of Two- Dimensional Solid Mechanics Problems 542  10.1 Torsion of Members with Arbitrary Cross- Section Shape 542  10.2 Plane- Stress Formulation 558  10.3 Isoparametric Formulation: Using a Quadrilateral Element 566  10.4 Axisymmetric Formulation 573  10.5 Basic Failure Theories 575  10.6 Examples Using ANSYS 576  10.7 Verification of Results 598  Summary 598  References 600  Problems 600  11 Dynamic Problems 609  11.1 Review of Dynamics 609  11.2 Review of Vibration of Mechanical and Structural Systems 623  11.3 Lagrange’s Equations 640  11.4 Finite Element Formulation of Axial Members 642  11.5 Finite Element Formulation of Beams and Frames 651  11.6 Examples Using ANSYS 665  Summary 684  References 684  Problems 684  12 Analysis of Fluid Mechanics Problems 691  12.1 Direct Formulation of Flow Through Pipes 691  12.2 Ideal Fluid Flow 703  12.3 Groundwater Flow 709  12.4 Examples Using ANSYS 712  12.5 Verification of Results 733  Summary 734  References 735  Problems 736  13 Three- Dimensional Elements 741  13.1 The Four- Node Tetrahedral Element 741  13.2 Analysis of Three- Dimensional Solid Problems Using Four- Node  13.3 The Eight- Node Brick Element 749  13.4 The Ten- Node Tetrahedral Element 751  13.5 The Twenty- Node Brick Element 752  13.6 Examples of Three- Dimensional Elements in ANSYS 754  13.7 Basic Solid- Modeling Ideas 758  13.8 A Thermal Example Using ANSYS 769  13.9 A Structural Example Using ANSYS 786  Summary 799  References 799  Problems 799  Tetrahedral Elements 744  14 Design and Material Selection 808  14.1 Engineering Design Process 809  14.2 Material Selection 812  14.3 Electrical, Mechanical, and Thermophysical Properties of Materials 813  14.4 Common Solid Engineering Materials 815  14.5 Some Common Fluid Materials 822  Summary 824  References 824  Problems 824  15 Design Optimization 826  15.1 Introduction to Design Optimization 826  15.2 The Parametric Design Language of ANSYS 830  15.3 Examples of Batch Files 832  Summary 843  References 844  Problems 844  Appendix A mechanical Properties of some materials 845  Appendix B thermophysical Properties of some materials 848  Appendix C Properties of Common line and Area shapes 849  Appendix D Geometrical Properties of structural steel shapes 852  Appendix e Conversion Factors 856  Appendix F An introduction to mAtlAB 858  index 893