Preface

 Acknowledgments

 1 Introduction

 1.1 Engineering Problems

 1.2 Numerical Methods

 1.3 A Brief History of the Finite Element Method and ANSYS

 1.4 Basic Steps in the Finite Element Method

 1.5 Direct Formulation

 1.6 Minimum Total Potential Energy Formulation

 1.7 Weighted Residual Formulations

 1.8 Verification of Results

 1.9 Understanding the Problem

 Summary

 References

 Problems

 2 Matrix Algebra

 2.1 Basic Definitions

 2.2 Matrix Addition or Subtraction

 2.3 Matrix Multiplication

 2.4 Partitioning of a Matrix

 2.5 Transpose of a Matrix

 2.6 Determinant of a Matrix

 2.7 Solutions of Simultaneous Linear Equations

 2.8 Inverse of a Matrix

 2.9 Eigenvalues and Eigenvectors

 2.10 Using MATLAB to Manipulate Matrices

 2.11 Using Excel to Manipulate Matrices

2.12 Solutions of Simultaneous Nonlinear Equations

 Summary

 References

 Problems

 3 Trusses

 3.1 Definition of a Truss

 3.2 Finite Element Formulation

 3.3 Space Trusses

 3.4 Overview of the ANSYS Program

3.5 ANSYS Workbench Enviornment

 3.6 Examples Using ANSYS

 3.7 Verification of Results

 Summary

 References

 Problems

 4 Axial members, Beams, and Frames

 4.1 Members Under Axial Loading

 4.2 Beams

 4.3 Finite Element Formulation of Beams

 4.4 Finite Element Formulation of Frames

 4.5 Three- Dimensional Beam Element

 4.6 An Example Using ANSYS

 4.7 Verification of Results

 Summary

 References

 Problems

 5 One- Dimensional Elements

 5.1 Linear Elements

 5.2 Quadratic Elements

 5.3 Cubic Elements

 5.4 Global, Local, and Natural Coordinates

 5.5 Isoparametric Elements

 5.6 Numerical Integration: Gauss—Legendre Quadrature

 5.7 Examples of One- Dimensional Elements in ANSYS

 Summary

 References

 Problems

 6 Analysis of One- Dimensional Problems

 6.1 Heat Transfer Problems

 6.2 A Fluid Mechanics Problem

 6.3 An Example Using ANSYS

 6.4 Verification of Results

6.5 Members Under Axial Loading with Temperature Change

 Summary

 References

 Problems

 7 Two- Dimensional Elements

 7.1 Rectangular Elements

 7.2 Quadratic Quadrilateral Elements

 7.3 Linear Triangular Elements

 7.4 Quadratic Triangular Elements

 7.5 Axisymmetric Elements

 7.6 Isoparametric Elements

 7.7 Two- Dimensional Integrals: Gauss–Legendre Quadrature

 7.8 Examples of Two- Dimensional Elements in ANSYS

 Summary

 References

 Problems

 8 More Ansys

 8.1 ANSYS Program

 8.2 ANSYS Database and Files

 8.3 Creating a Finite Element Model with ANSYS: Preprocessing

 8.4 h- Method Versus p- Method

 8.5 Applying Boundary Conditions, Loads, and the Solution

 8.6 Results of Your Finite Element Model: Postprocessing

 8.7 Selection Options

 8.8 Graphics Capabilities

 8.9 Error- Estimation Procedures

 8.10 ANSYS Workbench Environment

 8.11  An Example Problem

 Summary

 References

 9 Analysis of Two- Dimensional Heat Transfer Problems

 9.1 General Conduction Problems

 9.2 Formulation with Rectangular Elements

 9.3 Formulation with Triangular Elements

 9.4 Axisymmetric Formulation of Three- Dimensional Problems

 9.5 Unsteady Heat Transfer

 9.6 Conduction Elements used by ANSYS

 9.7 Examples Using ANSYS

 9.8 Verification of Results

 Summary

 References

 Problems

 10 Analysis of Two- Dimensional Solid Mechanics Problems

 10.1 Torsion of Members with Arbitrary Cross- Section Shape

 10.2 Plane- Stress Formulation

 10.3 Isoparametric Formulation: Using a Quadrilateral Element

 10.4 Axisymmetric Formulation

 10.5 Basic Failure Theories

 10.6 Examples Using ANSYS

 10.7 Verification of Results

 Summary

 References

 Problems

 11 Dynamic Problems

 11.1 Review of Dynamics

 11.2 Review of Vibration of Mechanical and Structural Systems

 11.3 Lagrange’s Equations

 11.4 Finite Element Formulation of Axial Members

 11.5 Finite Element Formulation of Beams and Frames

 11.6 Examples Using ANSYS

 Summary

 References

 Problems

 12 Analysis of Fluid Mechanics Problems

 12.1 Direct Formulation of Flow Through Pipes

 12.2 Ideal Fluid Flow

 12.3 Groundwater Flow

 12.4 Examples Using ANSYS

 12.5 Verification of Results

 Summary

 References

 Problems

 13 Three- Dimensional Elements

 13.1 The Four- Node Tetrahedral Element

 13.2 Analysis of Three- Dimensional Solid Problems Using Four- Node

 13.3 The Eight- Node Brick Element

 13.4 The Ten- Node Tetrahedral Element

 13.5 The Twenty- Node Brick Element

 13.6 Examples of Three- Dimensional Elements in ANSYS

 13.7 Basic Solid- Modeling Ideas

 13.8 A Thermal Example Using ANSYS

 13.9 A Structural Example Using ANSYS

 Summary

 References

 Problems

 Tetrahedral Elements

 14 Design and Material Selection

 14.1 Engineering Design Process

 14.2 Material Selection

 14.3 Electrical, Mechanical, and Thermophysical Properties of Materials

 14.4 Common Solid Engineering Materials

 14.5 Some Common Fluid Materials

 Summary

 References

 Problems

 15 Design Optimization

 15.1 Introduction to Design Optimization

 15.2 The Parametric Design Language of ANSYS

 15.3 Examples of Batch Files

 Summary

 References

 Problems

Appendix A mechanical Properties of some materials

Appendix B thermophysical Properties of some materials

Appendix C Properties of Common line and Area shapes

Appendix D Geometrical Properties of structural steel shapes

Appendix E ANSYS Workbench Environment and Examples

Appendix F An introduction to MATLAB

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