Finite element AnAlysis. A Primer

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