Finite Element Analysis: A Primer

✍ Scribed by Sarhan M. Musa

• Publisher: Mercury Learning and Information
• Year: 2023
• Tongue: English
• Leaves: 613
• Edition: 2
• Category: Library

✦ Synopsis

Finite Element Analysis, second edition is a comprehensive guide that explores the versatility and affordability of the finite element method (FEM) as a powerful tool for solving engineering problems across various industries. This book provides a practical introduction to FEM analysis, covering applications in mechanical engineering, civil engineering, electrical engineering, and physics. It presents a balanced blend of theory and applications, catering to both beginners and those seeking to enhance their FEM skills. The book emphasizes a comparative approach by presenting solutions to problems through three different methods: analytical, FEM hand calculations, and software-based methods. This enables readers to grasp the strengths and limitations of each approach, enhancing their understanding of FEM techniques.

FEATURES:

• Covering mathematical preliminaries to advanced engineering applications, the book covers a wide range of topics, including axial loaded members, trusses, beams, stress analysis, thermal analysis, fluid flow analysis, dynamic analysis, and engineering electromagnetics analysis
• Includes a comparison of solutions to the problems obtained by the analytical method, FEM hand calculations, and the software method
• Includes over 35 solved problems using software applications such as MATLAB, COMSOL, and ANSYS
• Features companion files containing executable models and animations related to each solved problem.

✦ Table of Contents

Cover
Half-Title
Title
Copyright
Dedication
Contents
Preface
Chapter 1: Mathematical Preliminaries
1.1 Introduction
1.2 Matrix Definition
1.3 Types of Matrices
1.4 Addition or Subtraction of Matrices
1.5 Multiplication of a Matrix by Scalar
1.6 Multiplication of a Matrix by Another Matrix
1.7 Rules of Matrix Multiplications
1.8 Transpose of a Matrix Multiplication
1.9 Trace of a Matrix
1.10 Differentiation of a Matrix
1.11 Integration of a Matrix
1.12 Equality of Matrices
1.13 Determinant of a Matrix
1.14 Direct Methods for Linear Systems
1.15 Gaussian Elimination Method
1.16 Cramer’s Rule
1.17 Inverse of a Matrix
1.18 Vector Analysis
1.19 Eigenvalues and Eigenvectors
1.20 Using Matlab
Exercises
References
Chapter 2: Introduction to the Finite Element Method
2.1 Introduction
2.2 Methods of Solving Engineering Problems
2.2.1 Experimental Method
2.2.2 Analytical Method
2.2.3 Numerical Method
2.3 Procedure of Finite Element Analysis (Related to Structural Problems)
2.4 Methods of Prescribing Boundary Conditions
2.4.1 Elimination Method
2.4.2 Penalty Method
2.4.3 Multipoint Constrains Method
2.5 Practical Applications of Finite Element Analysis
2.6 Finite Element Analysis Software Package
2.7 Finite Element Analysis for Structure
2.8 Types of Elements
2.9 Direct Method for Linear Spring
Exercises
References
Chapter 3: Finite Element Analysis of Axially Loaded Members
3.1 Introduction
3.1.1 Two-Node Bar Element
3.1.2 Three-Node Bar Element
3.2 Bars of Constant Cross-Section Area
3.3 Bars of Varying Cross-Section Area
3.4 Stepped Bar
Exercises
References
Chapter 4: Finite Element Analysis Trusses
4.1 Introduction
4.2 Truss
Exercises
References
Chapter 5: Finite Element Analysis of Beams
5.1 Introduction
5.2 Simply Supported Beams
5.3 Cantilever Beams
Exercises
References
Chapter 6: Stress Analysis of a Rectangular Plate With a Circular Hole
6.1 Introduction
6.2 A Rectangular Plate with a Circular Hole
Exercises
References
Chapter 7: Thermal Analysis
7.1 Introduction
7.2 Procedure of Finite Element Analysis (Related to Thermal Problems)
7.3 One-Dimensional Heat Conduction
7.4 Two-Dimensional Problem with Conduction and with Convection Boundary Conditions
Exercises
References
Chapter 8: Fluid Flow Analysis
8.1 Introduction
8.2 Procedure of Finite Element Analysis (Related to Fluid Flow Problems)
8.3 Potential Flow Over a Cylinder
8.4 Potential Flow Around an Airfoil
Exercises
References
Chapter 9: Dynamic Analysis
9.1 Introduction
9.2 Procedure of Finite Element Analysis (Related to Dynamic Problems)
9.3 Fixed-Fixed Beam for Natural Frequency Determination
9.4 Transverse Vibrations of a Cantilever Beam
9.5 Fixed-Fixed Beam Subjected to Forcing Function
9.6 Axial Vibrations of a Bar
9.7 Bar Subjected to Forcing Function
Exercises
References
Chapter 10: Engineering Electromagnetics Analysis
10.1 Introduction to Electromagnetics
10.2 Maxwell’s Equations and Continuity Equation
10.2.1 Maxwell’s Equations and Continuity Equation in Differential Form
10.2.2 Maxwell’s Equations and Continuity Equation in Integral Form
10.2.3 Divergence and Stokes Theorems
10.2.4 Maxwell’s Equations and Continuity Equation in Quasi-Statics Case
10.2.5 Maxwell’s Equations and Continuity Equation in Statics Case
10.2.6 Maxwell’s Equations and Continuity Equation in Source-Free Regions of Space Case
10.2.7 Maxwell’s Equations and Continuity Equation in Time-Harmonic Fields Case
10.3 Lorentz Force Law and Continuity Equation
10.4 Constitutive Relations
10.5 Potential Equations
10.6 Boundary Conditions
10.7 Laws for Static Fields in Unbounded Regions
10.7.1 Coulomb’s Law and Field Intensity
10.7.2 Bio-Savart’s Law and Field Intensity
10.8 Electromagnetic Energy and Power Flow
10.9 Loss in Medium
10.10 Skin Depth
10.11 Poisson’s and Laplace’s Equations
10.12 Wave Equations
10.13 Electromagnetic Analysis
10.13.1 One-Dimensional Elements
10.13.1.1 The Approach to FEM Standard Steps Procedure
10.13.1.2 Application to Poisson’s Equation in One-Dimension
10.13.1.3 Natural Coordinates in One Dimension
10.13.2 Two-Dimensional Elements
10.13.2.1 Applications of FEM to Electrostatic Problems
10.14 Automatic Mesh Generation
10.14.1 Rectangular Domains
10.14.2 Arbitrary Domains
10.15 Higher-Order Elements
10.15.1 Pascal Triangle
10.15.2 Local Coordinates
10.15.3 Shape Functions
10.15.4 Fundamental Matrices
10.16 Three-Dimensional Element
10.17 Finite Element Methods for External Problems
10.17.1 Infinite Element Method
10.17.2 Boundary Element Method
10.17.3 Absorbing Boundary Conditions
10.18 Modeling and Simulation of Shielded Microstrip Lines with COMSOL Multiphysics
10.18.1 Rectangular Cross-Section Transmission Line
10.18.2 Square Cross-Section Transmission Line
10.18.3 Rectangular Line with Diamondwise Structure
10.18.4 A Single-Strip Shielded Transmission Line
10.19 Multistrip Transmission Lines
10.19.1 Double-Strip Shielded Transmission Line
10.19.2 Three-Strip Line
10.19.3 Six-Strip Line
10.19.4 Eight-Strip Line
10.20 Solenoid Actuator Analysis with Ansys
Exercises
References
Appendix A: Ansys
Appendix B: Matlab
Appendix C: Comsol Multiphysics
Appendix D: 4-COlor Figures From the Text (On the companion files)
Index